Cameron John had equalised in the second half for Rovers after Lincoln took the lead against the run of play through John Akinde, who also missed a penalty.
And Rovers punished the miss as Tottenham loanee Kazaiah Sterling grabbed his first goal for the club with a superb Alfie May volley rounding off the win.
Having had a blank weekend due to the expulsion of scheduled opponents Bury from the EFL, Darren Moore made just two changes from the side that beat the Imps in the league 10 days earlier.
Speculation grew before kick-off that Lincoln’s management team of Danny and Nicky Cowley had been approached by Sheffield Wednesday over their managerial vacancy.
But the brothers were vocal presences in the technical area as they watched their current side concede much of the attacking play.
Despite being outworked in the opening period, the Cowleys will have been the happier at the break after Lincoln took the lead against the run of play two minutes from the break.
Akinde outsmarted John in receiving a ball inside the box and turning, before drilling beyond the helpless Seny Dieng.
Rovers were level when Ben Sheaf flicked on a corner, which Grant parried only for John to poke home from close range.
Akinde wasted a glorious opportunity to put his side back in front after being bundled over by John in the box.
After a stuttering run up, his penalty was saved by Dieng.
Rovers looked to immediately punish the miss with Ben Whiteman smashing a superb volley which Grant held well.
But the hosts did complete the turnaround on 69 minutes when substitute Sterling put them in front. May powered to the byline and stabbed a cross with Sterling placing his header beyond Smith.
Ten minutes later, the win was sealed as May rifled home first time after a corner was cleared out to the edge of the box.
Doncaster Rovers: Dieng; Halliday, Anderson, John, James; Whiteman, Sheaf (Blair 62); Sadlier, Coppinger (Taylor 46), May; Ennis (Sterling 62). Unused substitutes: Lawlor, Amos, Longbottom, Kiwomya.
Lincoln City: Smith, O’Connor (Payne 62), Bolger, Andrade, Chapman, Bostwick (Toffolo 46), Grant (Walker 63), Connolly, Melbourne, Akinde, Anderson. Unused substitutes: Vickers, Sault, Bucci, Al-Oyouni.
Referee: S Oldham (Lancashire).