The home side had the earliest chances, with Oscar shooting over the crossbar from close range before John Terry headed the club in front. Terry later left the pitch with a serious-looking injury.
Liverpool improved after the break and scored their equaliser through Luis Suarez, but there was to be no further scoring, as the two sides took a point apiece from the encounter.
The result leaves Chelsea in third and Liverpool 13th in the table.
Here are six things we learned from the game.
Brendan Rodgers decided to switch, in terms of his league formation, from a 4-3-3 (or 4-2-1-3) to a 3-5-2 for the game at Stamford Bridge.
The change had the desired impact of negating almost entirely the effects of Chelsea's attacking midfield trio behind Fernando Torres, and the home side had very few clear chances. In fact, those which they did have, falling to Oscar and Juan Mata, came about because of defensive errors from the midfield.
Liverpool also managed to out-number Chelsea in the midfield in the first half, resulting in their usual large amount of possession time, but the Reds were rather blunted in attack and were unable to get numbers into the final third with any regularity.
The better play in attack for the Reds came after the switch back to their normal formation after the introduction of Suso, in place of Nuri Sahin.
Liverpool picked up their sixth draw of the Premier League season at Stamford Bridge, a 1-1 scoreline at the home of the current European champions, which, on the face of it, is not a bad result, taken in isolation.
Of course, every game can be taken on its own merits, though. Did Liverpool pick up a valuable point here, or merely drop two more as they have done so often this season already?
Considering that Chelsea were ahead and looked the more dangerous side in the first half, and the Reds had to come from behind to claim a point, it can certainly be looked upon as a point won.
There's also the fact that the point from this weekend's game is a point back on catching up with some of Liverpool's rivals for a top-six spot, including Spurs and Newcastle United, both of whom suffered defeats on the same day Liverpool drew.
Luis Suarez headed in Liverpool's goal from close range against Chelsea, scoring his eighth league goal of the season in the process and putting him atop the Premiership's list of scorers.
That's ahead of Demba Ba, Edin Dzeko, Jermain Defoe and any other forward you care to mention—level only with Robin van Persie.
Suarez now totals 10 goals in all competitions (15 matches for the Reds), well on his way to bettering last season's total of 17 in all competitions.
At what point will people begin to accept he is a goal threat and a potent striker rather than criticising him for missing other opportunities?
With Liverpool employing wing-backs against Chelsea, as well as two more centralised attackers in the final third, neither Stewart Downing nor Oussama Assaidi were named in the starting lineup for the Premier League once more.
This is nothing particularly new; Downing has not started since the opening day in league matches, while Assaidi has still not started in the Premier League, making just two sub appearances so far.
Both were named on the substitutes bench by Brendan Rodgers, though, yet neither were called upon to help Liverpool win the game, even after they switched to playing two wide attackers later on in the match.
With left-back Jose Enrique playing as the most advanced player down that particular flank, both players must be wondering if they are going to get a chance any time soon to impress in the league.
Downing at least put in a good performance versus Anzhi in the Europa League during the week, but Assaidi was left as sub for that game, too; he has featured very little for the Reds in the past month.
Liverpool didn't win again at Chelsea, but they did manage to extend their unbeaten league run.
The Reds are now six Premier League games in a row undefeated since their unfortunate loss to Manchester United. In that time, they've beaten Reading and Norwich, whilst picking up a point against Newcastle, Stoke, Everton and now Chelsea.
It's clear that—aside from remaining unbeaten for as long as possible—Liverpool need to start converting draws into wins, but not losing is always important.
Wigan at home next week is a game Liverpool really need to take three points from. If they do, it will take the Reds up to the two-month mark of not losing in league action.
Liverpool have three long-term absentees at present because of injury: Lucas Leiva, Fabio Borini and Martin Kelly.
Added to that list of late has been goalkeeper Jose Manuel Reina and, against Chelsea, Martin Skrtel because of illness.
Reds captain Steven Gerrard suffered a brief injury during the course of the match against Chelsea and Brendan Rodgers stated that he might have a mild problem with his medial ligaments, though should be fine to play for England by mid-week.
Jonjo Shelvey, also in the England squad, missed out on the Chelsea squad because of injury, and there have also been talks that Daniel Agger suffered a slight injury during the game.
Liverpool's squad is small enough as it is without suffering further absences through knocks, and Rodgers will be glad his troops have a week before the next game—and he will also hope nobody new picks up injuries on international duty this coming week.