Sebastian Vettel set the fastest time in the Red Bull-Renault car in Singapore.
Vettel, who narrowly beat teammate Webber for the fastest time, set the time in the second practice session, after the track had dried out from the rain earlier in the week, which affected the first session.
McLaren driver Jenson Button was third in the second session, but was over one second behind Vettel. Mark Webber had earlier set the fastest time in the first practice session earlier at the Singapore street circuit.
After rain hit Singapore this week, the track was still recovering for Friday practice, which saw many drivers set only installation laps and then retreat back into the pits.
While he was out, Kubica was the first to experience the 'Singapore Sling' (as the chicane is now known at turn 10), going slightly left and off the track.
Christian Klien, test driver for Hispania replacing Yamamoto after the Japanese driver suffered from food poisoning, set the initial fastest time on the damp track with a 2:18.621, which was beaten by Vitaly Petrov 22 minutes into the session by just over two seconds.
Klien then regained the fastest time by going over a second faster than the Renault driver.
Petrov then returned to the top spot by five seconds from a Hispania car that has been uncompetitive so far this season, while Michael Schumacher entered the Singapore street circuit for the first time and set a time that was good enough to earn him second place, two seconds off the pace.
Buemi set a timed lap for Toro Rosso that gained him third place just under half an hour into the session, while both Petrov and Schumacher improved times, leaving the German driver on the top of the timesheets with an hour to go.
Timo Glock, who has finished in the top four in his last two races in Singapore, set the second fastest time, before going fastest in his Virgin Racing car.
Ferrari driver Felipe Massa went to fourth place, with Nico Hulkenberg slotting in behind as the track got darker.
Belgian driver Jérôme d'Ambrosio, who replaced Lucas di Grassi, set his first timed lap in his Virgin Racing car with a 2:17.100, leaving him in last place with 54 minutes remaining.
Bruno Senna went eighth fastest seconds later, while his compatriot Rubens Barrichello went into third place, before being beaten to that spot by his teammate at AT&T Williams.
While Bruno Senna and Jérôme d'Ambrosio battled for second-last place under the lights before jumping to seventh and eighth respectively, BMW Sauber driver Nick Heidfeld, who replaces Pedro de la Rosa for the rest of the season after leaving Pirelli, set the slowest lap of 2:18.898 in his first drive of the Sauber car this season.
Scuderia Toro Rosso driver Jaime Alguersuari set the fourth fastest time with 49 minutes to go, as Barrichello went second and Heidfeld went up into eighth.
Heidfeld then reached fifth position while his teammate Kobayashi set his first lap, leaving him in seventh.
Spanish driver (and DJ) Jaime Alguersuari set the fastest lap with a 2:00.655, a second quicker than anyone else, with half of the session remaining.
Petrov went second with a time that was one and a quarter seconds slower than the Toro Rosso, before being beaten to second place by Japanese driver Kobayashi, who then set the first time under two minutes with just over 40 minutes to go in the first session.
Michael Schumacher set a time in second place after being unable to overtake a Force India driver during the final sector of the lap.
Tonio Liuzzi went 10th in his Force India car, while his teammate Adrian Sutil set a time in 15th place and last from all the drivers who set a fastest lap in the first 37 minutes.
Liuzzi went sixth as Petrov went quickest, but Kobayashi then went quickest and Liuzzi moved up to fourth.
The Sauber driver then increased his gap to second placed Petrov, but Michael Schumacher set a faster time on his first outing on the Asian circuit.
Italian driver Liuzzi went up to third, while Force India teammate Sutil then beat Liuzzi to the third spot and Kobayashi set the quickest time as the track continued to dry out throughout the evening.
Unsurprisingly, the drivers who had set the most laps with just over 20 minutes to go were first and second.
Alguersuari went into seventh place, who was followed over the finish line soon after by Massa, who went into third place. Senna moved into 12th, while Timo Glock went into seventh before Alguersuari went into third.
As the track moved into the best conditions for slick tyres, Alonso set his fastest lap in cruise mode, which was 11 seconds behind the leader in the first two sectors, as they compared front noses.
Glock ran wide as Alguersuari reached second place and Button and Barrichello went out to set times.
Massa went fourth behind Michael Schumacher, while Glock went fifth and Malaysian driver Fairuz Fauzy set a time of 2:18.404 in his Lotus car.
His teammate Kovalainen moved 13th on his first lap, while Massa went second, Buemi went 14th and Button set his first timed lap in 10th. Rosberg went 15th in his first timed lap and Vettel went 18th.
Hamilton went 11th and Barrichello went ninth, as Webber went 11th, closely followed by Buemi, who went tenth, and Button, who moved into 11th. Heidfeld went 14th as the top contenders finally got up to speed and set competitive laps.
Sutil went second, but was moved down as Button moved into first place with five minutes remaining. As the rest of the field got faster and faster, Alguersuari went second and Sutil went first as he was overtaken by Lewis Hamilton.
Kobayashi moved into third as Button went fastest, before Vettel claimed the fastest time seconds later.
Schumacher went third as Webber was held up by Klien and backed off, while Alguersuari went second as the chequered flag came out, signalling the end of the session. Schumacher went fastest on his final lap, but was beaten by Mark Webber by 0.119 of a second with a 1:54.589.
In the second session, Alguersuari set the first time in his Toro Rosso with a 1:53.406, which was already faster than the times set in the morning.
As Kobayashi spun in his Sauber, Hulkenberg went second Buemi third. Lewis Hamilton set the quickest of the early times, while Barrichello went seventh. Force India driver Liuzzi moved up to fifth.
Massa ventured into the top three, followed by Jenson Button in fourth, while Adrian Sutil went second. Jaime Alguersuari went fastest with Button second, while Sutil went third.
Schumacher was in 13th as his teammate Rosberg went out of the track, while Barrichello went fastest.
Button set the first time of the weekend to go under one minute and 50 seconds with a time of 1:49.768, while Rosberg went into third and Alonso in second.
Alonso went fastest, while Webber moved into fifth position on the harder tyre. Kubica then went fifth while Buemi moved into thirteenth on his first run. Vettel moved to the top, before beating his own time, with Webber in third place.
Hulkenberg completed a good lap to go fourth. Webber moved into second after losing time in the middle sector.
Kubica set his best time of the session to go fourth quickest, before Button took it away from the Polish driver. Rosberg then moved up to 13th, with Hamilton up to ninth.
Schumacher moved up to seventh, 1.4 seconds behind Vettel, while Sutil drove back into the pits after damaging the front left part of his car.
Alonso moved within 0.2 seconds of Vettel's time, while Petrov went up to 12th. Button then set the fastest time on super-soft tyres, before Vettel went top once again.
Schumacher moved up to ninth as his compatriot Vettel improved his time. Klien rejoined the session in 23rd place, with Hispania Racing nine seconds off the fastest time.
Hamilton moved up to fourth position, before Webber moved to second place behind his teammate, showing the Red Bull's dominance at higher downforce circuits.
Hulkenberg posted some good sector times but went back into the pits, staying 11th. As Alonso stalled and got out of his car, Vettel moved back onto the track, but no one could beat him as all the competitive cars moved on to practice on higher fuel loads for the start of the race, leaving Vettel with the fastest time of 1:46.660, with Webber second and Button third.
On this evidence, it seems that Red Bull have the advantage this weekend.