Pep Guardiola's side had the chance to prolong the Reds' 30-year wait at least until the two sides meet at the Etihad Stadium next week, but the title was within touching distance when Christian Pulisic gave Frank Lampard's side a 36th-minute lead.
Kevin De Bruyne's spectacular free-kick brought City level and Raheem Sterling hit the post, but their vulnerability on the break was eventually punished when Fernandinho handled in a desperate 75th-minute goalmouth scramble.
The veteran Brazil international was sent off and his countryman Willian sealed the points and crowned Jurgen Klopp's dominant league winners.
Kepa Arrizabalaga acrobatically pushed Fernandinho's header from Riyad Mahrez's free-kick over the crossbar amid a controlled opening half-hour from City.
Ederson saved well from Pulisic and Andreas Christensen in quick succession at the other end, and he merited better protection when Chelsea took the lead.
Poor communication between Ilkay Gundogan and Benjamin Mendy and the latter's botched recovery tackle that left Pulisic in the clear to finish coolly.
There was questionable wisdom in Mendy seeking to atone for his errors by shooting frequently from distance early in the second half.
In the 55th minute, De Bruyne added finesse to that tactic with a sumptuous dipping free-kick after N'Golo Kante clumsily fouled Mahrez.
A one-touch counter-attack then ended with Sterling dinking against the post, with Chelsea's efforts noticeably more laboured.
Ederson launched that attack but a poor pass out was almost punished as Mason Mount thumped into the side netting.
City's slick dominance of the ball but creaky defence lent an intriguing balance to the final quarter of the contest – Sterling curling agonisingly wide before Kyle Walker somehow got back to improbably deny Pulisic a second on the goal line.
Fernandinho was unable to be so precise when denying Tammy Abraham, leaving Willian to send Ederson the wrong way and prompt celebrations on Merseyside.
What does it mean: Chelsea take important step towards the Champions League
Although most of the focus was understandable on the main consequence of this Chelsea victory, it was a huge three points for the Stamford Bridge side. Their five-point advantage over a resurgent Manchester United in fifth is restored, while a wobbling Leicester City are now just a point better off with seven matches remaining.
De Bruyne shows his class once again
It feels like a trick of the mind that City won a thrilling title battle last season with De Bruyne reduced to a bit-part role by two medial knee ligament injuries. He has performed at a level above his colleagues this time around, with his free-kick here another champagne moment that adds weight to his case for end-of-season honours.
Mendy's moment to forget
In the build-up to this match, Mendy spoke of how this was his "time" and how he wanted to show people "the real Mendy" following his injury nightmare. Presumably, the slapstick version on display for Chelsea's opener was not what he had in mind. Guardiola needs a more reliable left-back next season, in terms of both form and fitness.
Liverpool will emerge at the Etihad Stadium as champions, with the main bit of pre-match intrigue now set to revolve around whether a guard of honour is workable in the age of social distancing. Before that, City and Chelsea have away FA Cup quarter-finals on Sunday at Newcastle United and Leicester respectively.