McIndoe should have had a hat-trick but missed a sitter in the second minute when he volleyed wide from close range after Lewis Guy had set up the chance.
Blackpool were second best from start to finish and the only surprise was that Doncaster did not have more goals to show for their dominance.
Paul Heffernan fired just over the top in the seventh minute and McIndoe rattled an angled shot just wide a minute later, before Richard Offiong blasted a shot against the post in the 14th minute.
Heffernan made the breakthrough four minutes later when he produced a lethal left-foot shot from 15 yards after McIndoe and Guy had combined to set up the chance.
The Blackpool goal led a charmed life and the visitors were fortunate when Heffernan hit the post in the 24th minute after beating keeper Les Pogliacomi following good work by Guy.
Blackpool were rarely seen as an attacking force but skipper Peter Clarke headed over the top following a 34th-minute corner.
The Seasiders were fortunate to be only one goal down at the interval but their luck ran out in the second half.
McIndoe converted a 53rd-minute penalty after Clarke was adjudged to have handled a shot from Guy, and he blasted home another spot-kick three minutes later after Danny Warrender brought down the dangerous Guy.
Heffernan clinched the issue in the 72nd minute after linking with Guy who produced a superb cross for him to bundle the ball home from close range.
Blackpool battled to the finish and Jan Budtz did well to tip a header round the post from John Murphy, who was also unlucky to see another attempt brilliantly cleared off the line by Sean McDaid.
Clarke scored a consolation from the penalty spot in injury-time after Dave Mulligan had brought down substitute Rory Prendergast but, by then the tie was over.