The Sky Blues are unbeaten in five matches and despite going behind to a DJ Campbell strike in the first half, they hit two goals in five minutes to take the points.
Chris Coleman's squad has been ravaged by injury and illness and with just two fit professional defenders, he was forced to move midfielder Aron Gunnarsson to centre-back and hand a league debut to 17-year-old Curtis Wynter at right-back.
The Sky Blues threatened early on with a low-drive from Guillaume Beuzelin testing Paul Rachubka, but their backline was soon under pressure.
In the 23rd minute, a pass from debutant Campbell put Ben Burgess through on goal only for Gunnarsson to block his shot with a last-gasp tackle.
A minute later, Campbell fired another warning shot but his effort was high of Keiren Westwood's bar.
But City ran out of lives in the 25th minute when Burgess sent a lofted pass over the defence for Campbell to run on to and after shaking off Gunnarsson's advances, he slid the ball past Westwood.
Blackpool continued to push but failed to test Westwood again in the half.
Coleman's frustration was evident throughout the opening period but his half-time teamtalk helped turn the game on its head.
In the 47th minute, Jay Tabb's clever cross left the Seasiders' defence in a muddle and Beuzelin smashed home the loose ball to level.
Then a superb piece of hold-up play by Clinton Morrison freed Michael Mifsud to run onto a pass and put home his second of the season.
Blackpool looked deflated but had a late surge as they tried to level. Roy O'Donovan connected with a corner in the 84th minute only for it to be cleared off the line.
And the visitors thought they had got the equaliser minutes later when Campbell tapped home Graeme Owens shot but the linesman ruled the goal offside.