Goals from Mat Sadler and Carlton Morris either side of the break looked to have put the impressive Shrews on course for a comfortable victory.
While the six previous visitors to the New Meadow had failed to score, Rovers ended that run in dramatic style as Mathieu Baudry headed them back into the game before a controversial Dean Henderson own goal saw the visitiors draw level.
After a first half spent firmly on the back foot, few would have predicted how well Rovers would rally after the break, particularly after falling two goals down.
But they showed excellent resolve and determination to draw level and earn a superb point which stretches their unbeaten league run to seven matches.
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Darren Ferguson made two changes to the side that drew with Plymouth Argyle with Ben Whiteman and Joe Wright restored to the starting XI in place of Alfie Beestin and Mathieu Baudry.
Baudry would not have to wait long to get back on the pitch however as he replaced the injured Andy Butler just 11 minutes in.
Butler limped off after injuring himself in a challenge on Carlton Morris which brought Shrewsbury's first chance of the game as Morris headed over from the subsequent free kick.
Rovers really struggled to cope with Shrewsbury's hard press throughout the first half.
It denied them space when in possession and kept them firmly on the back foot. Bad decision making on the ball only ensured the pressure remained high.
It looked set to be a very long afternoon when Shrewsbury took the lead midway through the first half.
Ian Lawlor failed to get a good connection with a punch attempt from Shaun Whalley's corner and the ball fell to Sadler who hooked home from six yards.
Shrewsbury continued to push and Lawlor was forced into a fine save from Alex Rodman while Sadler drilled narrowly over the bar from the subsequent corner.
Ferguson sent on Alfie Beestin at the break, reshuffling into the midfield diamond.
A stunning stop from Lawlor prevented Shrewsbury from doubling their lead soon after the restart. Towering centre half Aristote Nsiala powered a header on goal from a corner only for Lawlor to stick out a hand and stop it on the line.
Rovers threatened on the counterattack with Beestin surging down the left and drilling a low ball which came out to Niall Mason who lashed wide from the edge of the box.
Shrewsbury doubled their advantage however on 53 minutes.
Nsiala headed down from a corner and Morris smashed in from close range.
Though it looked as though Rovers had a mountain to climb, they quickly made the ascent more gentle.
Baudry darted to the near post to meet Coppinger's corner and bundled a header home from close range.
And they were certainly the side in the ascent, forcing the issue.
Rovers reshuffled again with Issam Ben Khemis replacing Jordan Houghton to give the side an injection of creativity.
And it paid off as Rovers drew level.
Ben Khemis delivered a testing ball to the back post, Henderson rose and claimed but took a step back under pressure, carrying it over the line.
Both sides pushed for the winner but the momentum was with Rovers.
And in the final act of the game Baudry dropped a header from a corner on the roof of the net as Rovers threatened to seal a remarkable win.
Shrewsbury: Henderson, Hendrie (Payne 87), Nsiala, Sadler, Lowe, Godfrey, Whalley, Ogogo, Nolan, Rodman (Beckles 72), Morris. Subs not used: MacGillivrary, Gnahoua, Bolton, John-Lewis, Morris. .
Rovers: Lawlor, Blair, Wright, Butler (Baudry 11), Mason, Whiteman, Houghton (Ben Khemis 70), Kongolo (Beestin 46), Coppinger, Rowe, Marquis. Subs not used: Marosi, Garratt, Mandeville, May.
Referee: Anthony Backhouse (Cumbria)
Attendance: 5,818 (502 away)