Goals from Charley Kendall, Teddy Bishop and Anthony Scully gave the League One side their first win over Rovers in 18 years and sent McSheffrey’s men out of the competition at the first-round stage.
A bad day at the office was made worse by three fans running onto the pitch from the Polypipe Stand following Lincoln’s third goal, which meant the restart was delayed.
Here's out player ratings after Doncaster were outclassed in defence and attack.
1. Jonathan Mitchell - 5
A difficult night for the keeper, who was beaten three times. Might have been out a bit quicker for the opening goal. Got down well to get a hand to Maguire's strike in the second half, unlucky to then see the ball then roll into the path of Anthony Scully for a tap-in. Photo: Bruce Rollinson
2. James Maxwell - 5
Looked brightest when going forward but like many of his teammates couldn't find a bit of quality when needed. Photo: Howard Roe/AHPIX LTD
3. Kyle Knoyle - 5
The opening goal came from his side. Struggled to get forward as Doncaster were largely outplayed across the pitch. Photo: Howard Roe/AHPIX LTD
4. Adam Long - 5
Looked steady in the first half but not a memorable first start as the team shipped three goals. Photo: HOWARD ROE