Rovers, who made nine changes from Saturday’s 1-0 loss to Swindon Town, rekindled their useful habit of scoring late goals when Adam Long got the final touch to send the ball over the line for the winner with just six minutes left on the clock.
Kyle Hurst had earlier got Doncaster level with a super strike from the edge of the box after Lincoln took the lead through Charles Vernam's close-range header shortly after the half-time interval.
The win snaps a three-game losing streak for Gary McSheffrey's side and puts them top of the table in Group E with one game left to play.
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2. Louis Jones - 6
Appeared to tip a Lincoln effort over the bar in the first half but a goal kick was given. Made another smart low stop at the start of the second half but might have done better with the goal, which he got a touch on before it went in. Photo: Howard Roe/ahpix.com
3. Charlie Seaman - 6
Looked useful going forward at times but probably didn't do enough to give Gary McSheffrey too much of a selection headache in the coming weeks. Photo: Howard Roe/ahpix.com
4. James Maxwell - 6
Beaten by his man just before the opening goal, which dampened a largely decent display somewhat. Photo: HOWARD ROE