Kevin Phillips scored a stoppage-time penalty to earn Blackpool an FA Cup fourth-round replay.
Clinton Morrison, one of eight changes to the Sheffield Wednesday side, put them ahead against the run of play with an exquisite chip.
Blackpool had the best of the chances but Robert Harris and Phillips missed clear opportunities.
However, Gary Taylor-Fletcher was hauled down by Danny Batth and Phillips fired home from the spot late on.
Blackpool boss Ian Holloway, who also made eight changes, went on the attack from the off with the backing of their biggest crowd of the season.
In an entertaining first half full-back Harris twice tried his luck from distance, while Matt Phillips brought a save out of Wednesday goalkeeper Stephen Bywater with a low drive.
Phillips could have scored soon after the half-hour mark when, having cleverly engineered space, he shot inches wide.
Blackpool were made to pay for their poor finishing when Morrison gave the Owls the lead.
David Prutton's through ball found Ryan Lowe, who, in attempting to round goalkeeper Matt Gilks, found Morrison. He finished clinically from an acute angle.
The Seasiders struggled to fashion clear opportunities, but got their reward in the 91st minute, securing a replay that neither of these promotion-chasing sides will relish.
Sheffield Wednesday boss Gary Megson:
"I'm really disappointed, not surprised but disappointed. I thought that was the only way they were going to score, unless it was something special from distance.
"If it was a penalty it looked really soft, I didn't think it was. You saw from both line-ups what the competition is, we both want to go through but obviously there is an importance attached to the league fixtures, but the game was played in a proper competitive spirit.
"It was a little bit nip and tuck, we wanted to try and get the result away from home but once we did score we wanted to keep hold of what we've got.
"One of the problems with the FA Cup for teams like ourselves is each time we get through a round we have to postpone a game and we're near enough playing Tuesday, Saturday for the next few weeks."