Boss Gary McSheffrey went on the defensive following Saturday’s 4-0 defeat at Portsmouth and the ploy paid dividends as the Imps failed to break down Rovers’ resolute and reinforced rearguard.
Centre back Ro-Shaun Williams returned to the side at the expense of Joe Dodoo as McSheffrey went five back at the back and got men behind the ball.
Rovers barely created a chance all evening but completed a smash and grad raid when Dan Gardner slammed home a 75th minute penalty awarded for handball.
The victory was Rovers’ third win out of four on the road and moved them off the bottom of the League One table and to within six points of safety.
Speaking to BBC Radio Sheffield afterwards, McSheffrey said: “Obviously I’m pleased. It wasn’t pretty.
"I said we need to find a way to stop leaking goals and we just tweaked the shape and sat in a bit of a medium to low block and soaked it up.
"Lincoln are relentless in how they play and we made them force the play a little bit.
"We rode our luck a couple of times. Their full backs are good, lots of pace and good end product.
"But we defended well for large periods. We need to be a lot better on the ball when we when win it back.
"We could’ve hurt them quite a few times in the first half if we had a bit more composure and better quality in our first pass after winning the ball back. We were sloppy and rushing things.
"But as far the game plan went it worked. We didn’t create much but we obviously got the one opportunity and Dan stepped up and put it away.”