Sonny Bradley headed over for the visitors early on before fellow centre-half Tom Hamer registered the game's first effort on target although Thimothee Lo-Tutala was more than equal to it.
The visitors then had a golden chance to open the scoring when Harry Clifton felled Jack Moylan inside the area. Ex-Rovers loan star Rob Street stepped up but could only produce a tame penalty that Lo-Tutala did well to get down and push to safety. Rovers then thought they should have had a spot-kick of their own minutes later when the ball appeared to strike Tendayi Darikwa's arm, only for the referee to wave away appeals.
The hosts had defended stoutly all half and just when it looked as though their resistance would last until the interval, the Imps scored a quick, counter-attacking goal. Ben House fired into the bottom-left corner after the visitors pounced on a Matty Pearson botched clearance and worked it quickly from right to left.
Lincoln thought they'd doubled their advantage just after the restart when a header was glanced into the net among a crowded area but it was quickly chalked off for a foul on Matty Pearson.
The dominance of the visitors continued and their second eventually came when a throw-in was flicked on and found House who thumped home a header for his and the Imps' second. From that point on it seemed merely a case of how many Michael Skubala's men would get as they bombed forward at will. Street's frustrations continued as he hit a post prior to his late withdrawal but this was to prove to be Lincoln's night in a game they pretty much dominated from start to finish.
Here's how we rated the Rovers players on a tough night in DN4:
9. Hakeeb Adelakun 6
Another performance littered with ups and downs. Some nice moments but let himself down with bad decision-making, including second half when he blazed over with people waiting in the box. Frustrating showing. Photo: Howard Roe/AHPIX LTD
10. Brandon Hanlan 6
Back in the XI and had the bit between his teeth in the first half. Fought plenty and showed good close control, as he operated mostly off the right. Got tougher second half as the ball found him less and less. Photo: Andrew Roe/AHPIX LTD
11. Elliot Lee 7
Nice little touches around the corner but just shorn of enough time or space to make magic happen. Stuck to his task gamely, though. Photo: Craig Hawkhead / AHPIX LTD
12. George Broadbent 6
On as a replacement for Gotts at the break. Performed ok with some good passes in the few moments Rovers had chance to break forward. Photo: Andrew Roe/AHPIX LTD