Sergio Aguero fired home in the 10th minute and a second from Yaya Toure gave City a comfortable half-time advantage against the visitors, for whom Luis Suarez sat out the first of his eight-game ban after the Reds opted not to appeal.
City had midfielder Gareth Barry sent off late in the second half for a second bookable offence but increased their lead moments later through a James Milner penalty after Martin Skrtel fouled Toure.
Jermain Defoe marked his first Premier League start in over a month with a 63rd-minute winner as Tottenham kept the pressure on at the top with a 1-0 win over West Brom at White Hart Lane.
Harry Redknapp's men held out with ease against a Baggies side who seldom managed to threaten Brad Friedel in the Tottenham goal.
Sunderland continued their dramatic revival under new boss Martin O'Neill after a fine second-half display earned them a 4-1 win at Wigan and a place in the top half of the table.
Craig Gardner put the Black Cats ahead against the run of play in first-half injury time and James McClean headed a second 10 minutes into the second half before Wigan reduced the deficit through Hugo Rodallega.
But Sunderland - for whom defeat at home to Wigan had cost O'Neill's predecessor Steve Bruce his job - stormed back to secure victory through further goals from Stephane Sessegnon and David Vaughan.
On Monday, Arsenal conceded two late goals to lose to Fulham 2-1 at Craven Cottage, while Frank Lampard struck in the 89th minute to hand Chelsea a 2-1 win over Wolves.
Nathan Dyer and Wayne Routledge helped Swansea to a 2-0 win over Aston Villa at Villa Park, their first away victory of the season, while Stoke beat Blackburn 2-1 thanks to a Peter Crouch brace.
Joey Barton opened the scoring for QPR in their home game against Norwich but then proceeded to get sent off, paving the way for the Canaries to steal a 2-1 win thanks to goals from Anthony Pilkington and Steve Morison.
On Wednesday, Manchester United will look to bounce back from last Saturday's 3-2 loss to Blackburn when they travel to Newcastle, while Everton entertain Bolton.
Tuesday's Premier League Results
Man City 3-0 Liverpool
Tottenham 1-0 West Brom
Wigan 1-4 Sunderland
Wednesday's Premier League Fixtures
Newcastle vs Man United
Everton vs Bolton
Monday's Premier League Results
Fulham 2-1 Arsenal
Wolves 1-2 Chelsea
Aston Villa 0-2 Swansea
QPR 1-2 Norwich
Blackburn 1-2 Stoke