Reading striker Sam Baldock struck a post in the first half before Blackpool took the lead shortly before the half-hour mark through Nathan Delfouneso.
Baldock equalised 11 minutes into the second half, but Armand Gnanduillet restored the Blackpool advantage four minutes later.
Danny Loader made it 2-2 with a clever backheel, but Gnanduillet wasted the chance for a Blackpool victory when his chipped penalty struck the crossbar.
In-form Reading, FA Cup semi-finalists in 2015, had won four successive Championship matches over the festive period to move to within six points of the play-offs.
But manager Mark Bowen decided to change his entire starting XI from the team that triumphed 2-1 at Fulham on New Year's Day.
Blackpool, cup winners in 1953, lie two points off the play-off places in the third tier.
They were without a win in five matches but boss Simon Grayson made only four changes from the 2-1 defeat at Rotherham on Wednesday.
Blackpool, who had defeated Morecambe and non-league Maidstone United to reach the third round, began slowly.
Reading dominated the early exchanges, with Garath McCleary blazing over after cutting in from the right flank.
Blackpool offered little going forward, though a dangerous cross from Liam Feeney was well intercepted by home goalkeeper Sam Walker.
Reading upped the tempo and almost went ahead when Baldock's clever flick struck Blackpool keeper Mark Howard and deflected behind off a post.
But Blackpool replied positively and made it 1-0 in the 28th minute from their first meaningful attack.
Gnanduillet nodded down a cross from Calum MacDonald and Delfouneso stooped to head home from close range.
Blackpool began brightly in the second period, with Delfouneso going close to adding his second goal.
He broke free of the Reading cover but his eventual shot lacked accuracy and Walker saved comfortably.
Reading levelled in the 56th minute when Baldock latched on to a pass from Michael Olise and drove a fierce first-time effort past Howard.
But their parity lasted only four minutes, with Gnanduillet lashing in his 15th goal of the season from a tight angle.
Reading equalised in the 66th minute, when substitute Loader's cheeky backheel from a McCleary cross went in off an upright.
Blackpool had the chance to again go in front, two minutes later, when Teddy Howe clumsily fouled Gnanduillet in the area.
The French-born striker's Panenka penalty had Walker beaten but clattered against the bar and was cleared to safety after a scramble.
Walker also saved a late point-black effort from Delfouneso to force the replay at Bloomfield Road.