The Citizens struggled to find their rhythm for large parts and came close to falling a goal down in the second half, only for a penalty call in their favour to swing things in the closing 18 minutes.
Hull, with just one win in their last 16 league games and without a clean sheet in that time, gave their all to pull off an upset, but in the end City did enough to pick up a win that takes them back within seven points of leaders Chelsea.
Man City were dealt a blow less than 15 minutes in when John Stones picked up a knock and had to be replaced, only going to further disrupt a backline that had again shown a couple of changes from last time out.
The first half never truly got going but both sides did have half-chances to edge in front, with Jake Livermore heading over from eight yards out before being denied by Claudio Bravo, while David Silva was thwarted by Marshall from further out.
Nolito was the next to try his luck from the edge of the area, sending another tame attempt down low for Marshall to comfortably keep out as the Tigers saw out the opening 45 minutes with their goal yet to be breached.
Hull had found themselves four goals down at this stage the last time the two teams met on Boxing Day - that 2008 fixture now best remembered for manager Phil Brown's on-pitch team talk at the midway stage.
There was nothing one-sided about this match until the final 20 minutes or so, however, as Hull gave it all they had in the second half, albeit after Kevin De Bruyne - named as City's sole striker this evening - sent a curled shot against the frame of the goal.
It was then Hull's turn to come within inches of finding that key breakthrough goal when Michael Dawson saw his header cleared off the line by a backtracking Bacary Sagna just short of the hour mark - a big moment in the match.
The Tigers were seeing more of the ball as things transpired but Man City did show signs of moving through the gears, with substitute Kelechi Iheanacho seeing an attempt blocked by Marshall shortly before the pivotal moment arrived.
After cutting inside from the right Raheem Sterling was felled by Andrew Robertson inside the box, leading to referee Bobby Madley pointing to the spot and Toure calmly sending Marshall the wrong way - the Ivorian now converting from all 10 pens he has taken in the Premier League.
A quick-fire second was added by Iheanacho six minutes later, rounding off a slick counter which saw De Bruyne slip in Silva who squared the ball for his teammate to maintain his impressive goals-per-minute ratio.
It was then a case of the under-par visitors seeing out the remainder, with a Robert Snodgrass free kick down the middle the only save Bravo had to make, before Curtis Davies put into his own net from the final act after Sterling blasted the ball across the face of goal.