City will travel to Anfield for a crunch clash on Sunday week and Manuel Pellegrini knew his men could afford no mistakes in Saturday's early kick-off, having dropped two points at Arsenal last time out.
Yaya Toure and Rickie Lambert traded penalties in the first half before Saints - and England - suffered a significant blow, with Jay Rodriguez stretchered off due to a knee injury.
City were able to take a two-goal advantage into the half-time interval, as a controversial Samir Nasri strike and an Edin Dzeko header put them firmly in the ascendancy.
After the break, substitute Stevan Jovetic made victory certain before Toure hit a post late on.
City got off to a perfect start when Toure netted his 18th league goal of the season - and 22nd in total - from the penalty spot after just three minutes.
Jose Fonte fouled Edin Dzeko in the area and referee Chris Foy had no hesitation in pointing to the spot, despite Saints claims that the Bosnian had exaggerated the contact.
City could have doubled their lead moments later as they created a clear-cut opportunity for Nasri, but the Frenchman's low drive flew narrowly wide.
It was then Saints' turn to impress as they went in hunt of an equaliser. Rodriguez almost picked out Lambert with a dangerous cross and Adam Lallana was unlucky not to bring a ball under control when well placed. Lambert was only just off-target from a free-kick, while City threatened again when Jesus Navas sliced wide after an appeal for handball against Dejan Lovren was denied.
In the 26th minute, play was held up when Rodriguez went down in considerable agony, clutching his knee, after landing heavily when unchallenged. The 24-year-old was eventually carried off, to generous applause, on a stretcher, but there were fears his season - and World Cup chances - could be over.
City went close again as Dzeko thumped a header against the bar from Nasri's floated free-kick.
Foy had another easy spot-kick call eight minutes before the break. Pablo Zabaleta dangled out a leg right in the corner of the box and Jack Cork went down - allowing Lambert to rifle home from 12 yards and keep his perfect Saints penalty record intact.
However, City restored - and then increased - their advantage on the cusp of half-time.
Toure fed Dzeko, whose classy flick found David Silva. The Spaniard kept his composure in the box and slid a perfect pass for Nasri to finish first time. Television replays, however, showed Silva was in an offside position by a considerable distance.
As Mauricio Pochettino complained to the officials, Saints were quickly undone again as Silva found the overlapping Aleksandar Kolarov - in for Gael Clichy in the only City change from the 1-1 draw at the Emirates - and the Serbian's whipped cross was met by Dzeko's thumping header.
The visitors thumped Newcastle 4-0 in their previous outing but had been forced to bring in Paulo Gazzaniga in goal following an injury to Artur Boruc, while Morgan Schneiderlin replaced James Ward-Prowse in the starting line-up.
Saints' 22-year-old Argentinian goalkeeper saved from Dzeko and Navas in the second half, but he was to concede a fourth goal in the 81st minute.
City worked the ball from left to right at the back and Vincent Kompany picked out Navas, whose first-time cross eluded everyone - including a grasping Gazzaniga - leaving Jovetic with an empty net to tap into.
There was still time for Toure to hit a post from the edge of box as the hosts eased towards a crucial victory.
Ahead of Chelsea's clash with Stoke on Saturday night, City climb to second spot, a point behind Liverpool with a game in hand.