The Algerian came on as a first-half sub for the injured Kevin De Bruyne and bagged a priceless winner ten minutes after the restart to send City back to the top of the Premier League for at least 24 hours.
The Cherries failed to register a single shot on target and, but for keeper Artur Boruc, would have been beaten by a heavier scoreline.
The first-half was probably as dull as the Blues have been involved with this season and reminiscent of an attack versus defence training session.
Bournemouth, with six defenders named in their starting XI, pretty much camped in and around their own box, asking City to solve the puzzle.
There was no space to operate in as the Cherries’ smothering tactics had a similar effect to Chelsea’s in the first half of the Carabao Cup final.
The best chance fell to David Silva on 19 minutes as Bernardo found De Bruyne on the right of the box and his low cross was side-footed wide by the Spaniard from 10 yards.
Thereafter fell a couple of half-chances with Nicolas Otamendi spectacularly sending an overhead kick just over from the edge of the box and a tame John Stones header registering the first shot on target not long after.
De Bruyne pulled up with what could be a hamstring injury – though at this stage unconfirmed – on the stroke of half-time and was replaced by Mahrez.
Mahrez’s first half injury time corner caused a scramble in the six-yard box, but the Blues were again crowded out by a Bournemouth defence who looked determined and resolute.
City’s injury concerns worsened just after the re-start when Stones was replaced by Vincent Kompany, though it was later proved to be more of a precautionary move.
The Blues had stepped up the pace and one or two more gaps were appearing and on 55 minutes – at last – came the breakthrough.
Zinchenko’s dinked a pass to Silva eventually nudged the ball right for Mahrez to hit a low shot past Artur Boruc.
The relief was palpable both on the pitch and among the travelling City fans who celebrated wildly.
The hosts would surely now have to abandon their defensive shackles and be more adventurous – and in doing so open up spaces that the Blues could exploit - and to a certain extent, they did.
On 65 minutes, City quickly counter-attacked and Bernardo released Sterling to fire a low shot that Boruc pushed around the post.
Sterling then teed up Aguero on 69 minutes, but Boruc saved his toe-poked effort with the Blues looking to kill the game off.
Thirteen minutes from time, David Simpson’s poor backwards header was collected by Sterling, but Boruc was again quick off his line to deny the City winger - and Mahrez skied the loose ball.
And four minutes after that Aguero came within a whisker of doubling the advantage with a deft cross-cum-shot that was tipped onto the underside of the bar by Boruc.
Boruc saved well again on 86 minutes as Mahrez’s powerful header from a corner was beaten out as the Cherries clung on for dear life.
As it transpired, the hosts’ lack of imagination meant Ederson was a spectator for virtually the entire game and City comfortably ran down the minutes that remained to claim three crucial points.
Blues show resilient side
Two goals in three games may not be the free-scoring City we are used to, but in each match the opposition have focused on stopping City playing.
We may not be used to seeing our players running the clock down near the corner flag in added time, but the champions are doing what it takes to get the job done.
And anyone who thinks this or the win over West Ham was fortunate need only look at the stats.
Today. City had 23 shots and Bournemouth none - the hosts set their stall out and ultimately you'd have to say it was purely damage limitation - anything other than a victory for the Blues would have been cruel.
What it means…
City go two points clear of Liverpool who face Everton at Goodison Park tomorrow afternoon.
Star man: Oleksandr Zinchenko
Yet another impressive display by the neat and tidy Ukrainian.
“It was an incredible performance, one of best played in our time together.
“Ten players behind the ball for every moment, second balls, set pieces, everybody focused on controlling… it is a joy and pleasure to be part of this team.
“Thank you to my players who were absolutely incredible. It doesn't matter what happens at the end of season, these players deserve my admiration."
The Blues can rest up with no midweek game.
City host Watford at the Etihad Stadium next Saturday.