The victory ensured the National League champions and FA Cup quarter-finalists rounded off the calendar year in League Two’s automatic promotion places.
Striker Matt Rhead continued his excellent form with both goals in a game which Lincoln should have won by a far greater margin, given their dominance.
The first goal arrived in the eighth minute when a wonderful cross from Neal Eardley was headed home by a diving Rhead.
However, Rovers equalised on 24 minutes as Lincoln conceded their first goal in the league for more than a month. The visitors’ leading scoring, Christian Doige, was the man to find the net, crashing the ball beyond Josh Vickers after a smart turn in the box.
The Imps continued to dominate after the break and Rhead restored their lead when Harry Anderson’s ball into the box found the striker, who coolly lifted it over keeper Bradley Collins in the 57th minute.
Doige almost scored another equaliser in the 89th minute, only to be denied by a stunning reaction save from Josh Vickers.
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