A goal to the good courtesy of Mallik Wilks' clinical 51st-minute finish, the Tigers may have been on the back foot when disaster struck late on at the KCOM Stadium, but they looked pretty comfortable defending their slender advantage.
There seemed no danger on the cards when Richie Smallwood rolled the ball back towards Reece Burke near halfway, however the latter's slip allowed Ben Woodburn to seize possession and scamper away towards George Long's goal.
The City centre-half did his best to recover and get back into a position where he could attempt to atone for his initial error, only to succeed in hauling the on-loan Liverpool youngster down just outside the home box.
The outcome was inevitable, and not long after referee Samuel Barrott brandished a 77th-minute red card in Burke's direction, Blackpool levelled matters through Jerry Yates' close-range strike at a corner.
Scenting blood, the Tangerines clearly fancied their chances of going on to complete the turnaround during the closing stages, though Grant McCann's team dug in and made it through to full-time without too many moments of serious concern.
Given the circumstances, a point against useful opposition isn't necessarily a shocking outcome, but the bigger picture is slightly more concerning.
Following on from their draw at Sunderland last weekend, Saturday represents another missed opportunity as more points went begging in a game where it could be argued that a team with a top-quality number nine in their ranks would have had all three.
Josh Magennis didn't miss the golden chances that Tom Eaves has spurned in recent weeks, though he looked off the pace and failed to even get on the end of a couple of very inviting deliveries into dangerous areas.
As a team, Hull have now won just once in their last seven League One outings, a run that has seen them pick up as few as six points from the 21 on offer. Promotion form it certainly is not, and although they remain second and within touching distance of leaders Lincoln, their title challenge appears to be faltering.
Plenty of positives can be taken from this weekend's overall footballing display, however, as particularly in the first 45, the home players passed and moved the ball intelligently.
Debutant Gavin Whyte drew a routine save out of Chris Maxwell, before getting on the end of George Honeyman's inch-perfect pass down the right to deliver a low cross from close to the byline that was begging to be finished off.
Another clever Honeyman pass released Wilks on the opposite flank, however City's mercurial winger pulled his attempted finish across goal and well wide of the upright.
Blackpool's Sully Kaikai blasted a shot narrowly past the post at the opposite end, while Ollie Turton failed to hit the target from a couple of yards out when he ought to have done much better.
The half ended with Jacob Greaves failing to find the target with a free-header from Honeyman's free-kick, though the second began with a big let-off.
A left-wing Blackpool corner was helped on by Gary Madine at the near post, but with the goal gaping and City skipper Smallwood in close attendance, Yates failed to apply the finishing touch.
Hull then got their noses in front when Honeyman's delightful pass in behind found Whyte raiding down the right wing.
Magennis couldn't control his team-mate's low centre on the penalty spot, but managed to tee up Wilks, who advanced from the left-hand side of the area to blast a fine strike across Maxwell and into the bottom corner.
There were chances for the Tigers to add to their lead, Greaves again unable to finish off another inviting Honeyman set-piece, before substitute Keane Lewis-Potter sent a free-kick just over the Blackpool cross-bar.
Burke's calamitous slip then saw the home team reduced to 10 men, and the Tangerines would capitalise on their numerical advantage, Yates ending a spell of pinball inside the six-yard-box with a close-range which leveled matters.
Hull City: Long; Emmanuel, Burke, Greaves, Elder; Honeyman, Smallwood, Docherty; Whyte (A Jones 79), Magennis (Lewis-Potter 72), Wilks. Unused substitutes: Ingram, Coyle, Slater, Chadwick, Salam.
Blackpool: Maxwell; Turton (Gabriel 82), Ekpiteta, Ballard, Husband (Garbutt 82); Lubala (Woodburn 63), Ward, Dougall (Robson 82), Kaikai (Virtue 58); Yates, Madine. Unused substitutes: Sims, Antwi.
Referee: S Barrott (West Yorkshire).