Rovers bowed out of the Carabao Cup after failing to convert their chances on a frustrating evening at Blundell Park.
A first-half sucker-punch from Jordan Cook decided the match, after the visitors had created by far the best chances of the opening period.
Rovers pushed in the second period, but could not find a way back into the game. Visiting manager Darren Moore made six changes from the side who lined up against Rochdale on Saturday, with Seny Dieng, Matty Blair, Ali Crawford, Alex Kiwomya, Niall Ennis and Cameron John all handed their first starts of the campaign.
Dieng got a nice early touch of the ball as he confidently plucked Luke Hendrie’s cross from the right out of the air for his first competitive action as a Rovers player.
Rovers created the best chances in the opening period, with James McKeown in the home goal having to get down quickly to stop a Kieran Sadlier delivery and also be alert 10 minutes later to hold Ennis’ ross
In-between those two chances came an opportunity for Kiwomya, who lifted the ball over after getting on the end of a pass from Ben Whiteman.
And Rovers’ skipper had two chances of his own which he could not keep down as Rovers confidently imposed themselves on the game - plus another effort from distance which went narrowly wide, all before the opening quarter of an hour had been concluded.
McKeown was by far the busiest of the two keepers, and had to be alert to dive low to his left to keep out a powerful Sadlier shot from distance. The resulting corner saw John stab the ball wide from Crawford’s free-kick.
The home side took the lead completely against the run of play with five minutes to go when they broke quickly and Jordan Cook slotted home.
McKeown had to be at his best to turn away a Sadlier effort immediately afterwards, while Cook was clearly energised by his goal as he tried an effort from distance which Dieng had to be at full stretch to keep out and ensure the score was only 1-0 at the break.
Rovers made one change at the break, bringing Sheaf on to replace Whiteman.
Sadlier flicked a header wide five minutes after the restart, but with the home side happy to defend chances were harder to come by.
Sadlier was consistently Rovers’ biggest threat, firing an effort wide and unleashing a thunderbolt after 68 minutes that McKeown did brilliantly to keep out. He could not hold on to the ball,
A Sadlier effort was stopped by McKeown, who could not hold the ball but Jon Taylor - who by now had replaced Alex Kiwomya - was flagged offside as he prepared to slot home.
Alfie May came on for the final 10 minutes, replacing Blair, and the No.19 was a threat - crossing for Ennis who tried an overhead kick and fired an effort wide on the volley himself.
Rovers pushed for an equaliser, with a Crawford effort from distance going over and only a late block stopping Ennis.
James lashed an effort from outside the area that was deflected wide in some last-ditch defending from the home defence, while from the resulting corner Dieng - who had come up for the set-piece - headed an effort that was blocked.