Only a massive swing in goal difference in Manchester United's favour in their rearranged fixture against AFC Bournemouth can now deny City and their incoming manager Pep Guardiola fourth place and with it a berth in the qualifiers for Europe's premier club competition.
As news that United's game had been delayed and subsequently abandoned after a suspect package was found inside Old Trafford filtered down to south Wales before kick-off, City just had to focus on their own job.
They are now all-but certain of achieving their objective after Kelechi Iheanacho's early strike, which was cancelled out on the stroke of half-time by Andre Ayew's deflected free-kick.
However, City's failings this season - they were touted as favourites for the Premier League title before a ball was kicked last August - were summed up in 90 frustrating minutes when they somehow failed to put Swansea to the sword.
It was the Swans' first game since Francesco Guidolin signed a two-year deal and they were in good form at home with four successive wins, their best run in five seasons of Premier League football.
But United's hope for some assistance was not helped by Swansea resting their four EURO 2016 players ahead of next month's tournament, and midfielder Ki Sung-yeung having returned to his native South Korea for four weeks of military service.
City had the perfect start after five minutes through Iheanacho's 14th goal of the season, even if there was an element of confusion about it.
Stand-in Swansea goalkeeper Kristoffer Nordfeldt pushed out Sergio Aguero's shot and Iheanacho appeared to be in an offside position when he pocketed the rebound.
But referee Mike Dean overruled his flagging assistant as Angel Rangel was still on the field of play to the right of the goal after his attempt to stop the initial cross.
Swansea were not so fortunate five minutes later when Dean adjudged that Jefferson Montero pushed Bacary Sagna at the far post before squirting the ball past Joe Hart.
It was a debatable decision, and one which City should have benefited from to build on their advantage.
But Nordfeldt saved from Kevin De Bruyne and Aguero and Swansea escaped again when Montero's misplaced backpass presented Iheanacho with a shooting opportunity he wasted.
Jesus Navas was also guilty of spurning a speedy counter-attack and City were punished for their profligacy on the stroke of half-time when Nicolas Otamendi brought down Leon Britton 25 yards out.
Ayew took over free-kick duties in the absence of usual taker Gylfi Sigurdsson and his effort struck the head of Fernando to change the direction of the ball and leave Hart stranded.
The second half started much as the first had been conducted with City on top but lacking a ruthless edge to their game.
Iheanacho was unable to control the ball with the goal at his mercy, and Aguero fired badly wide as he failed to draw level in the race for the Golden Boot with Tottenham Hotspur's Harry Kane.
Federico Fernandez headed wide from a corner, but Swansea were not to threaten again and City's race with United was effectively won.