Ian Holloway's in-form Seasiders have scored 13 goals in their last four league encounters and their extra firepower proved the difference against Doncaster, Yorkshire's top-ranked side, whose own hopes of a top-six finish were dealt a mighty blow.
Campbell, on loan from Leicester since early February, struck his third goal in two games from close range midway through the first half and Dobbie curled home a superb second with his first touch in the 67th minute soon after replacing the injured Hameur Bouazza.
Blackpool are now unbeaten in their last five matches, but Doncaster, beaten 2-1 at home by lowly Plymouth on Saturday, have taken only four points from their last five.
Campbell, Bouazza, David Vaughan and Stephen Crainey all returned for Blackpool, while Paul Heffernan, fresh from his loan spell at Bristol Rovers, was recalled by Rovers manager Sean O'Driscoll.
Charlie Adam was first to show for the home side, drilling an early 25-yard shot wide before Doncaster midfielder Mark Wilson volleyed narrowly off target from a half-cleared corner.
Both sides were swift on the counterattack and both Jay Emmanuel-Thomas and John Oster threatened with shots from outside the penalty area for the visitors before Blackpool took a 27th-minute lead through Campbell.
Crainey crossed into the area and Campbell, on loan from Leicester, pounced on the loose ball to stab home left-footed from close range.
Doncaster responded when Heffernan forced Blackpool goalkeeper Matthew Gilks into a full-length save with a fine header from Shelton Martis' cross.
The home side grew in confidence towards the end of the first half and Keith Southern, Bouazza and Ian Evatt all threatened to double their lead, while Heffernan had two shots blocked just before half-time.
Both sides created chances after the break. Gilks did well to hold Wilson's 20-yard effort and then Southern forced visiting goalkeeper Neil Sullivan into an even better save with a thumping drive.
It was end to end action. Rovers defender Gareth Roberts twice fired in shots that were blocked and Sullivan tipped over Bouazza's snap-shot from 12 yards at full stretch.
Doncaster were denied an equaliser by the woodwork when Hayter headed Roberts' pin-point cross against the crossbar in the 64th minute.
Bouazza was forced off soon after and was replaced by Dobbie, who wasted little time in firing Blackpool into a two-goal lead.
Vaughan played the ball into the penalty area from the left and Dobbie curled a fine right-footed shot inside Sullivan's far post from 12 yards in the 67th minute.
Doncaster continued to create openings though and James Coppinger's shot from inside the area was blocked by Evatt, but Rovers goalkeeper Sullivan saved well from Vaughan and Campbell as Blackpool chased a third.
Rovers sent on strikers Dean Shiels and Jordan Mutch in the 86th minute and although the latter brought the best out of Gilks with a low shot in the closing stages, Blackpool held on to their two-goal advantage.