Lewis Hamilton attempted to chase the German's lead down but finished second after an incident with Daniel Ricciardo in the pit lane drew a five-second penalty for the Briton and ultimately had a major bearing on the end result.
Mercedes' Valtteri Bottas clinched third spot after starting the race in pole position. Ferrari's Kimi Raikkonen and Red Bull's Daniel Ricciardo finished in fourth and fifth, respectively.
The official Formula One Twitter account provided a look at the final classification, where Max Verstappen was among the biggest losers following an early retirement, while Vettel streaked clear of the pack:
Here's how the drivers' standings look after Sunday's result:
|2017 Formula One Driver Standings|
|5||Max Verstappen||Red Bull||25|
|6||Daniel Ricciardo||Red Bull||22|
|8||Sergio Perez||Force India||14|
|9||Carlos Sainz||Toro Rosso||10|
|10||Romain Grosjean||Haas Ferrari||4|
|11||Kevin Magnussen||Haas Ferrari||4|
|12||Esteban Ocon||Force India||3|
|14||Daniil Kvyat||Toro Rosso||2|
|15||Antonio Giovinazzi||Sauber Ferrari||0|
|18||Marcus Ericsson||Sauber Ferrari||0|
Bottas took pole position in Saturday's qualifying session—his first since joining Mercedes for this season—and the Finn succeeded in defending his place at the head of the grid in the early laps.
Ferrari star Vettel remained tight on the leader's heels from the offset, with Hamilton and the Red Bull pair of Verstappen and Ricciardo close behind, as highlighted by the Telegraph:
It was Vettel who blinked first and pitted after much speculation regarding whether his team would employ a one- or two-stop approach, with the German's early change confirming Ferrari had opted for the latter.
Vettel's Ferrari team-mate Kimi Raikkonen moved past Felipe Massa and up to sixth, but Verstappen's race soon came to an end after the Dutchman entered the pits for the first time.
Red Bull's 19-year-old sensation returned to the track but swiftly encountered brake issues as his RB13 slid into the barriers on Lap 12, and Autosport Live noted Williams' Lance Stroll was another early casualty after a crash with Carlos Sainz:
Hamilton incurred a damaging five-second penalty for backing up Ricciardo on his way into the pits shortly after that incident, and the safety car played into Ferrari's hands as Vettel wrestled the lead upon the restart.
Ricciardo's change onto the softs hurt his chances after the Australian dropped down to sixth due to what seemed to be a lack of grip, with Raikkonen capitalising with a move to P4 and into podium contention.
Mercedes realised second-placed Bottas' super softs didn't stand as great a chance at victory as Hamilton, third, on the softs, and instructed their top man to pass his team-mate into second, per F1 on NBC Sports:
Thirty laps in and Vettel held an advantage of around five seconds over the Briton, who would likely be able to reach the end of the race on his current tyres, while the German would likely require a second pit stop.
Bottas pitted from third and emerged back at seventh before snaking his way up the order into fifth, and Vettel quickly followed, sacrificing his lead to Hamilton in order to switch onto the softs before returning in third place.
However, Pirelli Motorsport took heed of the fact Vettel wouldn't necessarily have to beat Hamilton to first in order to win the race:
Hamilton did make a second pit stop in spite of earlier predictions, losing an 11-second lead over Vettel and re-entering the fray at third behind his Mercedes team-mate, Bottas.
The three-time world champion questioned the decision to equip soft tyres instead of super-softs over the team radio, but Mercedes were then pleased to hear Hamilton gunning for the top yet again, with Vettel 16 seconds ahead of him, having served his five-second penalty during the second stop:
On the penultimate corner of the 47th lap, Hamilton again passed Bottas into second and was angling for leader Vettel, who was roughly 11 seconds ahead but had lost time to his British peer in the previous laps.
Sauber's Marcus Ericsson saw his day come to a premature end six laps from home due to a faulty gearbox just as Vettel began to approach the backmarkers in his crusade for first place.
Hamilton also started dodging his way through traffic as he lapped Jolyon Palmer, but the gap of nine seconds with only four laps remaining seemed too great to close down as he came into the race's finale.
And that turned out to be the case as Vettel pressed his advantage to end a five-year hoodoo in Bahrain:
Drivers now have a fortnight's rest before travelling to Sochi for the Russian Grand Prix on April 30, a race that's set to crown a new champion after retired champion Nico Rosberg won last year's edition.
However, Hamilton will be another ace to keep an eye on in the meeting considering he won Russian Grand Prix titles in 2015 and 2014, with the Briton angling for Mercedes' fourth successive victory in Russia later this month.