Edin Dzeko's 12th goal of the season put the hosts ahead midway through the first half only for Daniel Sturridge to smash home his fourth in six matches for Liverpool since his move from Chelsea.
An even better trademark Steven Gerrard strike put Liverpool ahead with 17 minutes to go only but Sergio Aguero salvaged a point with an exquisite shot from the narrowest of angles.
However, it was not enough on a weekend when rivals Manchester United won and the result leaves Roberto Mancini's side nine points adrift of the leaders.
Gareth Bale's superb strike earned Tottenham victory over 10-man West Brom at The Hawthorns - and closed the gap to third-placed Chelsea to one point.
The Wales international struck his 11th league goal of the campaign mid-way through the second half to end a run of three successive draws for Andre Villas-Boas' team.
Albion played the final 42 minutes with 10 men after defender Goran Popov was sent off for spitting in the direction of Spurs defender Kyle Walker.
Tottenham took full advantage of their numerical advantage to dominate the second period despite the loss of leading scorer Jermain Defoe with an ankle injury.
Bale was a constant threat with his pace and power as he followed up his mid-week equaliser at Norwich with another crucial goal.