Rovers missed the chance to register a fifth consecutive home win on a frustrating afternoon at Ewood Park.
It looked on course when Jordan Rhodes fired them in front after just 14 minutes, the striker notching his 12th of the campaign after good work from Craig Conway.
But the visitors made Rovers pay for their wastefulness in front of goal when they scored an unlikely equaliser three minutes before the break. Defender Grant Hall applying the finishing touch after Peter Clarke had headed on Jamie O'Hara's free-kick.
Blackpool then very nearly took the lead moments later when another O'Hara set-piece struck the post, Hall unable to capitalise on the rebound.
The frame of the Darwen End goal would prove to be Rovers' nemesis in the second half as again chances were created but not taken.
After Rhodes had put an overhead kick just wide, Rudy Gestede twice rattled the crossbar as the visitors goal lived a charmed life.
Rhodes was denied by Lewis in the closing stages, before substitute Chris Brown and Alex Baptiste wasted late opportunities to turn one point into three.
At a chilly Ewood Park the first half was very much about the home side not making the most of their opportunities, and the visitors taking theirs.
It had started well for Rovers with the returning Jordan Rhodes firing the blue and whites in front after just 14 minutes but they couldn't build on that.
The goal was made in no small part by the persistance of Craig Conway as the midfielder skipped into the box past despairing challenges. The Scot making his way to the byline before laying the ball on a plate for Rhodes to notch his 12th of the campaign from a couple of yards out.
Then after a one-two with Jay Spearing, the unlikely figure of Matt Kilgallon raced through on goal, but Joe Lewis in the Blackpool goal was sharply off his line to clear.
Rovers kept pressing and probing but without reward. Matt Kilgallon spectacularly fired over from a Tom Cairney free-kick, before Rhodes looked to add to his tally with a first-time effort that Lewis watched flash past his post.
Despite seeing plenty of the ball the home side were often wasteful in possession and that would come back to bite them as Blackpool scored an unlikely equaliser three minutes before the break.
From a free-kick just inside the Rovers half Jamie O'Hara sent the ball long into the box, captain Clarke flicked on and Grant Hall applied the finishing touch.
Two minutes later and the visitors were width of a post from going in front.
Again it was from a set-piece as O'Hara fizzed a low ball into the area, Steele watched on as it struck the post and rebounded off his chest, before being thankful that goalscorer Hall could only hit the side-netting on the follow-up.
After that mad few minutes Rovers went back to forcing the game on their opponents, but the Seasiders stood strong to keep the home side at bay as referee Mick Russell blew for half-time.
In a pattern similar to the first half, the second saw Rovers created more than enough chances, but frustratingly they weren't taken.
Rhodes went close with an overhead kick five minutes after the restart, the Rovers striker's effort was just wide after he met Grant Hanley's knockdown.
His strike-partner Gestede would go closer on 58 as his near post header from a Conway corner bounced off the crossbar with Blackpool scrambling the rebound away.
Then a superb ball into the box from Spearing was perfect for Rhodes but his glancing header cleared the goal.
When the woodwork was rattled once more you sensed it wasn't going to be Rovers' day as Gestede headed against the bar from a Cairney centre. It would prove to be his last involvement as cup hero Josh King replaced him.
Aside from a Gary Madine shot that found the side-netting, it was Rovers who remained camped in the opposition's half.
The closing stages saw further chances spurned, Rhodes saw a header glance wide and a shot saved. Whilst substitute Chris Brown fired wide of goal in added time.
Alex Baptiste could have won the match against his former club, but from Conway's centre he nodded wide of goal to sum up Rovers' day.
ROVERS: Steele, Baptiste, Hanley (c), Kilgallon, Spurr, Cairney, Spearing, Evans (sub Taylor 46 mins (sub Brown 80 mins)), Conway, Rhodes, Gestede (sub King 68 mins).
Subs not used: Eastwood (GK), Olsson, Williamson, Duffy.
Goals: Rhodes 14 mins.
BLACKPOOL: Lewis, Maher (sub Rothwell 68 mins), Hall, Clarke, Dunne, Ferguson, O'Hara, Perkins, Cameron (sub McMahon 53 mins), Telford (sub Delfouneso 60 mins), Madine.
Subs not used: Parish (GK), Cubero, Oliver, Osavi-Samuel.
Goals: Hall 42 mins.
Attendance: 14,906 (including 944 visiting supporters).