Rickie Lambert scored in injury time but Championship leaders Southampton lost their 21-match winning home run.
Lambert, back in the team after injury, gave the home side the lead at St Mary's with a deflected shot before Chris Basham levelled with a header.
The visitors went ahead when Saints goalkeeper Bartosz Bialkowski somehow allowed Callum McManaman's scuffed shot to squirm through his hands and legs.
But Lambert headed the late equaliser with his 16th goal of the season.
Bialkowski, starting his first league match in two years after regular number one Kelvin Davis was ruled out with a groin problem, looked nervous from the outset.
The 24-year-old Polish under-21 international spilt a cross from Matt Phillips behind for a corner with his first touch and then made an unconventional save with his chest to keep out Ludovic Sylvestre's snapshot.
Southampton took the lead when Adam Lallana dispossessed Neal Eardley, passed to Jack Cork, who fed Lambert and the striker's shot took a big deflection off Craig Cathcart and flew past Matt Gilks.
The Seasiders levelled after Basham found space at the back post to head home McManaman's cross and almost took the lead when Phillips' 20-yard shot hit the foot of the post, with Bialkowski rooted to the spot.
And the inexperienced keeper's day took a turn for the worse just after half-time.
McManaman went on a mazy run into the area but his shot was tame, and the winger had already turned away to trot back up the pitch.
However, the ball went through Bialkowski's legs and rolled over the line, despite the keeper's desperate attemps to claw it back.
Shell-shocked Saints went in search of an equaliser but Gilks saved from Guly do Prado, Dean Hammond curled a shot just wide and substitute Steve de Ridder volleyed over.
But in the 93rd minute Frazer Richardson crossed into the area and Lambert powered his header past Gilks to snatch a crucial point.
Southampton manager Nigel Adkins: "Bart is always outstanding in training and he will be a stronger character for what happened to him.
"We will support him and help him get over this mistake and the good thing is we did not lose the game.
"As for the record, it had to go some time. If you had said at the start of the season we would win 10 and draw the other of our first 11 home games I would have taken it without a moment's hesitation.
"Teams are taking no chances when they come to our ground now, as you would expect, so it is often hard to break them down but at the end we might even have got a third goal."
Blackpool manager Ian Holloway: "I don't know where the officials got five minutes extra (from). How on earth they reached that number I just don't know.
"It is a bitter pill for us to swallow because I thought we were going to win and nobody has done that down here for a year.
"In the end I've got to be satisfied with a good draw but we could so easily have won it and that's why it feels a little bit like a defeat."