Two years ago Leeds played poorly when they were beaten 3-0 by Watford in the Championship play-off final and, although United produced a better display this time, they were second-best for long spells, particularly in the opening 30 minutes of the game.
Jason Price fired over the bar in the eighth minute when he should really have scored before Richie Wellens fired into the side-netting when a cross would surely have been the better option.
Casper Ankergren then twice saved Leeds by racing out of his goal to deny first James Coppinger and then Hayter.
When Leeds finally settled the lively Jermaine Beckford, a former Scunthorpe loanee, shot straight at former Leeds keeper Neil Sullivan but it was Rovers that ended the first period strongly with Hayter once again going close to breaking the deadlock.
Doncaster finally scored the goal their good play deserved two minutes after the interval when the unmarked Hayter headed past Ankergren from virtually on the penalty spot.
Leeds tried to respond but they looked strangely disjointed despite Jonny Howson's promptings.
He fired a shot over the bar, but veteran keeper Sullivan was not called on to make any impressive saves as Rovers defended doggedly.