Largely lacking in the zippy play which delivered five consecutive wins, Rovers were made to work hard for their solitary point, particularly after falling behind midway through the first half.
Morecambe skipper Peter Murphy put the hardworking visitors in front after 24 minutes with John Marquis netting his 18th goal of the season to grab a second half equaliser.
Darren Ferguson unsurprisingly kept faith with personnel and system from the magnificent 3-0 win over Yeovil Town the previous week, opting again for 3-5-2.
Rovers had the ball in the back of the net within the first few minutes when Andy Williams clipped home following a rapid break only to be flagged offside.
Swift passing moves characterised Rovers' early play and they found plenty of space in the opposition half.
John Marquis blasted over from the edge of the box after another sweeping move which saw Matty Blair dart into the box and square.
Marquis then turned creator, playing a neat one-two with Tommy Rowe who scuffed his shot straight at Morecambe keeper Barry Roche.
The visitors forced their way into the game, enjoying particular success in wide areas where their wing backs operated high up the pitch.
They also had an effort ruled out for offside when a Michael Rose free kick drifted past Ian Lawlor, but the assistant referee spotted the Rovers keeper was unsighted by an advancing forward.
And Rovers had an effort cleared off the line. Roche raced out to block Williams but the ball fell to Grant who could only produce a tame effort which was hacked clear.
There was no questioning the finishing as Morecambe took the lead on 24 minutes.
Murphy scuffed his first touch after a corner kick fell to him but it was enough to confuse his marker and he curled a brilliant effort home from 15 yards.
Rovers pushed for an equaliser before the break as Marquis rise to meet a fine Blair cross only to head just over the bar.
And they drew a fine save from Roche as Williams side-footed first time a cross from Coppinger. Marquis' follow-up effort was also blocked.
With the final act of the half, Coppinger scuffed an effort straight at the keeper as Rovers' shooting continued to let them down.
Rovers emerged for the second half with renewed intent and pushed hard for the equaliser.
Coppinger curled wide from the edge of the box while more direct running from Blair caused plenty of headaches for Morecambe.
Blair almost grabbed a fortuitious goal when a cross was blocked but ricocheted back off him, forcing Roche into a fine reaction stop.
Grant curled a free kick over the bar from 20 yards as Rovers continued to push.
They got their reward on 56 minutes with the leveller.
While their finishing had let them down earlier in the game, there no questioning that of Marquis, who produced a deft first time effort to send a low ball into the bottom corner.
Ferguson threw on Liam Mandeville for his first appearance since New Year's Eve, looking for the winner.
And Rovers looked the more likely to get it. A fine ball from Houghton just flew over the head of Grant, poised at the back post.
Marquis smashed a brilliant effort narrowly wide from 25 yards as Rovers pushed.
But Lawlor had to be alert to keep out a shot from point blank range from substitute Rhys Turner as Morecambe threatened to nick the points.
Rovers pushed deep into six minutes of added time but could not find the opportunity they needed for the winner.
Rovers: Lawlor, Blair, Baudry, Butler, Mason, Rowe, Coppinger, Houghton (Middleton 90), Grant, Marquis, Williams (Mandeville 66). Subs not used: Etheridge, Wright, Alcock, Keegan, Beestin.
Morecambe: Roche, McGowan (Duckworth 85), Whitmore, Edwards, Kenyon, Molyneux, Murphy, Wildig (Evans 72), Rose, Ellison, Mullin (Turner 72). Subs not used: Nizic, Wakefield, Conlan, Jordan.
Referee: Eddie Ilderton (Tyne & Wear)
Attendance: 6,096 (184 away)