Daniels made save after save in the 120 minutes of Sunday's semi-final second leg at Gigg Lane to keep Bury at bay, saving a Phil Jevons penalty in normal time, before even more heroics in his side's 4-3 shootout victory.
It was an amazing turnaround for Paul Simpson's men as they were two minutes away from losing the tie - Bury had won 1-0 in the first leg at Shrewsbury - until Kevin McIntyre's 88th-minute strike levelled the tie.
Bury controlled the entire 30 minutes of extra time, but could not find a way past the inspired Daniels and his shootout saves from Danny Racchi and Andy Bishop secured Shrewsbury's place at Wembley.
The game started with both sides intent on playing attacking football and it was Bury that created the first opportunity after just five minutes when Morrell's neat shot on the turn was well saved by Daniels, before the former Blackpool striker had another effort saved soon after.
Bury were dominant and Alan Knill's men had a golden opportunity to extend their aggregate lead and finish the tie off after 33 minutes.
Neil Ashton, whose calamitous own goal handed Bury the advantage at the ProStar Stadium on Thursday, hauled down Morrell in the penalty area, but from the resulting spot-kick Jevons saw his casual effort saved by Daniels, who then reacted quickly to deny Michael Jones' follow-up effort.
The Shrews were boosted by their lucky escape and finished off an enthralling first half on top, having several chances to open the scoring and draw level on aggregate.
Firstly McIntyre shot wide from a good position, before Wayne Brown produced two fine stretching saves to keep out Paul Murray and Ben Davies efforts.
Bury resumed after the interval determined to control matters and Shrewsbury were again reliant on goalkeeper Daniels to keep them in the game when he produced another fine stop.
The ball broke to Jones on the left and he found Morrell, whose left-footed effort was destined for the bottom corner until the on-loan West Brom man got down low to block the effort.
Bury were rarely troubled throughout the second period and looked to be holding on, but just as they were beginning to dream of Wembley, Shrewsbury popped up with a goal out of the blue that levelled the tie with just three minutes remaining.
A loose ball fell to McIntyre on the edge of the area and he rifled into the bottom corner to send the game to extra time.
Shrewsbury were reduced to 10 men with virtually the first action of extra time, when Steve Leslie was dismissed for an aerial challenge on Stephen Dawson.
And Bury had several chances made their numerical advantage count, but Daniels was the hero again as he produced two top class saves to deny substitute Bishop and David Buchanan, while Darren Moss also cleared off the line.
The Shakers were swamping the Shrewsbury area and Bishop had two more gilt-edged chances to send his side through to the final but Daniels continued his outstanding work by saving both efforts.
Daniels was to make one last save, denying Bennett's effort with his feet as the game went to a penalty shootout.
And when Danny Racchi and Andy Bishop failed to beat Daniels, victory was confirmed for Shrewsbury, who reached their second play-off final in three years.
The Shrews will face Gillingham or Rochdale - who meet at Priestfield for the second leg later on Sunday after a 0-0 draw last week - at Wembley on Saturday May 23.