The Gulls carried a 2-0 advantage into the semi-final second leg from last Saturday's encounter at Plainmoor, but Shrews simply failed to do enough on home soil to threaten the aggregate scoreline.
Graham Turner's side struggled to create a single opportunity of note - indeed it was the visitors who enjoyed the better of what chances there were at the Greenhous Meadow, Chris Zebroski and Gavin Tomlin going closest.
It proved a disappointing way for Shrews to mark their 125th anniversary and the pre-match balloons and cake failed to inspire a turnaround, leaving them to reflect on a third failed play-off campaign in five seasons having narrowly missed out on automatic promotion.
Torquay, who finished the regular season in sixth, are now 90 minutes from promotion to the third tier in only their second season back in the Football League, registering what would be an impressive turnaround since being relegated from League One in 2005.
Gulls boss Paul Buckle kept faith with the same XI who triumphed in the first leg, while Shrews counterpart Turner made just the one change - winger Lionel Ainsworth coming in for striker James Collins, who dropped to the bench.
Town skipper Ian Sharps proved his fitness after thigh and groin problems and the influential centre-back showed his worth after just five minutes, getting across to block Jake Robinson - on a six-month loan from Shrews but eligible to feature against his parent club - after he found himself bearing down on goal having dispossessed right-back Jermaine Grandison.
All in all, the opening quarter was a frantic, scrappy affair with no inch given by either side.
Torquay's Scott Bevan was only called upon to keep out a couple of speculative efforts while the visitors threatened but lacked cutting edge in the final third - most notably when Tomlin flashed a low teasing ball right across the face of goal.
Zebroski forced the game's first real save in the 33rd minute, turning Nicky Wroe 25 yards out and slamming a fierce drive goalwards which Ben Smith palmed to safety.
Shrewsbury, toothless in attack, certainly started the second half with much more purpose but it was Torquay who should have put the tie beyond doubt in the 50th minute.
As in the first half, Grandison was caught in possession and Eunan O'Kane sent Tomlin through, he turned Shane Cansdell-Sherriff but could only curl his effort wide of the far post.
It was a more open affair after the break, but still, neither keeper was being tested enough.
Grandison blocked Robinson's goalbound effort before Tomlin blazed another clear opening wide with 20 minutes remaining.
Wroe, former Torquay captain, drilled a long-range effort which forced Bevan to tip over in the 88th minute but it was far too little too late as Shrews finished the campaign with a real whimper.