The Blackpool substitute was set up by Morgan Rogers to net the only goal of the game from close range just 12 minutes after coming on.
That leaves the Tangerines now just three points adrift of safety with two games left - but they might have to win both, at home to Millwall and away to Norwich to give themselves a chance.
Blackpool are now three points adrift of Neil Warnock's 21st-placed Huddersfield, who have a game in hand.
Both sides had shared five goalless draws this season, including the one between Blackpool and Blues at Bloomfield Road back on 10 December.
And this one looked like it may become another blank after the two sides managed just one shot on target between them before the break.
John Eustace's Blues, now safe from relegation themselves, looked more of a threat after the restart.
But they were made to pay for a dreadful mix-up between home defender Kevin Long and stand-in goalkeeper Neil Etheridge on 74 minutes which allowed Poveda to knock in the only goal.
It brought Blackpool's first away win since October, at Coventry, and Poveda his second only-goal-of-the-game matchwinner, having also scored in a 1-0 home win over Stoke City in February.
Blues,
who stay 17th, 10 points above the relegation zone, were again without
top scorer Scott Hogan with a groin injury - and boss John Eustace
confirmed that he will miss the final two games, as he is due to see a
specialist this week....<<<Read More>>>...
