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:
1. Thimothee Lo-Tutala 8
Good decision-making when coming for a few punches and then down well to keep out Street's early penalty. Was alert to most things, but powerless for House's goals. Photo: Howard Roe/AHPIX LTD
2. Jamie Sterry 6
Had his hands full as he tried to keep House in line. Did put in some good challenges on what was a busy night. Replaced for the final half-hour or so by Nixon Photo: Howard Roe/AHPIX LTD
3. Matty Pearson 7
Up against a crop of livewire Lincoln forwards. Sadly for him, his botched clearance was pounced on as Lincoln quickly countered to open the scoring. Recovered ably after that, though, with plenty of blocks and headers. Photo: Howard Roe/AHPIX LTD
4. Sean Grehan 6
Another start and another encouraging night. Hungry and alert to most dangers up against a really physical outfit, with ample headers won. Photo: Howard Roe/AHPIX LTD