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:
5. Jack Senior 6
Up against Rovers old boy Street - a battle you just know he relished. Carded first half. Linked up really well with Lee down his flank at times but was pinned back plenty all game. Photo: Howard Roe/AHPIX LTD
6. Owen Bailey 6
Skipper fluffed his lines early doors from inside the area. Bustled about plenty but had to chip in defensively as Lincoln bossed proceedings most of the night. Photo: Howard Roe/AHPIX LTD
7. Robbie Gotts 6
Not his most dominant performance but understandable against such strong opposition. Did put in a couple of well-timed tackles. Booked in first half and hooked at half-time. Photo: Andrew Roe/AHPIX LTD
8. Harry Clifton 5
Gave away the penalty as he up-ended Moylan in the box. Actually had few touches of the ball before he went off just after the hour. Photo: Howard Roe/AHPIX LTD