Vale worked hard early on to try and stop Doncaster from settling into their stride and it was a scrappy game for much of the first half.
Doncaster tried to force the pace and were unlucky not to score when Leo Fortune-West headed against the bar after out-jumping the visiting defence to connect with a great cross from Simon Marples.
James Coppinger lobbed just over the bar five minutes later after working a neat move with Ross McCormack, and Jason Price fired wide when well placed in the 23rd minute.
The bobbly pitch made good football difficult for both sides but Rovers seemed to adapt better and Fortune-West sent a glancing header wide in the 25th minute, before David Wheater had an effort saved at full stretch by Mark Goodlad minutes later.
Fortune-West got in the way of a shot from team-mate Price, giving Port Vale a fortunate escape in the 32nd minute.
Vale came into the game more just before the interval with Constantine hammering a shot into the side netting in the 39th minute, before Tony Dinning forced a fine save from Jan Budtz with a tremendous 25-yard effort.
McCormack should have made the breakthrough for Rovers on the stroke of half-time when he raced clean through but Goodlad came to the rescue again to tip away his low shot.
Michael Cummings hit a good chance for the visitors just over the top in the 48th minute after latching on to a loose clearance.
But it was Doncaster who ended the stalemate in the 58th minute when Fortune-West struck with a terrific 20-yard shot after Price and McCormack had combined to set up the chance.
McCormack had another effort cleared off the line by George Pilkington and Dave Mulligan had a goal-bound shot deflected for a corner.
Doncaster seemed to have done enough for victory, but paid the penalty for defending too deep when Constantine popped up to level the scores when he fired home at the far post after latching on to a superb left-wing cross from Craig James.