A fine first half goal from Armand Gnanduillet meant they had to settle for their sixth draw in eight league games.
The Black Cats did enough to win it, but Will Grigg missed two big opportunities on his home debut.
Stung into action by poor recent performances, Jack Ross freshened up his Sunderland side.
Lynden Gooch dropped into central midfield, with Duncan Watmore given freedom to drive forward from the right flank.
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The early response was encouraging, Grant Leadbitter going close with two efforts.
There was an intensity to Sunderland's play and they were unfortunate that Duncan Watmore's cross to the front post just evaded Will Grigg.
Even if Blackpool settled into the game thereafter, the home side looked the more likely and Jimmy Dunne came close when he surged forward from the halfway line unchallenged, eventually curling an effort just wide.
The game was turned on its head in a two-minute period half an hour in.
Jack Baldwin did superbly to spring his side onto the counter from a Blackpool corner, Watmore racing fee into the inside channel. He teed up Grigg in space but on his weaker side, the striker could only shoot straight at Mark Howard.
Within moments Armand Gnanduillet picked up the ball in space at the other end, rifling a long-range effort into the bottom corner.
The immediate response from the home side was good, with Luke O'Nien feeling he should have had a penalty
But the tension brought on by poor recent results began to take its toll, Sunderland losing their shape and playing into Blackpool's hands.
Defender Ben Heneghan should have made it two when he towered above his marker at a corner, heading over the bar from a matter of yards.
Matty Virtue then drew a good save from McLaughlin as the Black Cats went into the break desperately needing to regroup.
Blackpool were indignant early in the second half as Antony Evans tumbled in the box, the away side adamant he had been brought down by Gooch.
Gnanduillet went close with an effort from a narrow angle soon after and Ross had seen enough, throwing on Charlie Wyke.
Sunderland picked up, Watmore flashing a shot wide before Wyke tried to shoot on the turn as the ball broke into the box, slicing his effort away from trouble.
It had been a quiet night for Grigg, but with an hour on the clock he missed a second chance to score, this one a gilt-edged opening.
Baldwin had sprung him clear with an excellent ball through the middle and when he got to the ball first, rounding Howard, he looked certain to equalise.
With the goal gaping he somehow found the side netting.
Sunderland's attacking threat had improved significantly and it finally paid off with fifteen minutes to go.
Another excellent Leadbitter corner found Jack Baldwin, who emphatically headed past Howard.
The Black Cats continued to make all the running, despite the visitors slowing down the game at every opportunity.
Grigg went close when he headed a cross from substitute Tom Flanagan goalward, but Howard was able to save.
That late pressure wasn't enough to force a late winner as Sunderland missed another chance to make headway in the race for automatic promotion.
Sunderland XI: McLaughlin; O'Nien, Baldwin, Dunne, James (Flanagan, 78); Leadbitter, Honeyman; Watmore, Gooch (Wyke, 51), McGeady (Morgan, 61); Grigg
Subs: Ruiter, Maguire, McGeouch, Sterling
Blackpool XI: Howard; Evans (Long, 72), Heneghan, Tilt, Bola (Feeney, 7); Turton, Thompson, Pritchard, Virtue (Kirby, 90) Delfouneso, Gnanduillet
Subs: Dodoo, K Sorensen, Shaw, Mafoumbi
Bookings: Thompson, 79
Attendance: 27, 580