Haynes, who joined the Tykes from Bristol City last week, headed home a right-wing cross from Bobby Hassell nine minutes into the second half to give his side the lead at the Keepmoat Stadium.
An unusually subdued Doncaster struggled to respond and fell further behind 13 minutes later when Haynes cut in from the right and fired in a low left-footed shot that squirmed under the body of Neil Sullivan.
The visitors held on comfortably thereafter to record their first away win of 2011 and leapfrog their opponents in the Championship table.
Doncaster have now lost four consecutive games in all competitions and their misery was compounded by injuries to Mark Wilson, James Chambers and Matt Kilgallon.
Rovers manager Sean O'Driscoll named an unchanged side, while Barnsley skipper Jason Shackell returned from suspension to face his former club. Stephen Foster was also back from a ban for the visitors, so both Jim O'Brien and Diego Arismendi dropped to the bench.
Neither goalkeeper was seriously troubled in a lacklustre opening to the game.
However, Barnsley stopper Luke Steele had to react well to deny Billy Sharp in the 19th minute after the striker had hooked a right-footed shot towards the bottom-right corner.
The away team's attacking efforts were frequently halted by the offside flag as the half progressed, with Kieran Trippier the guilty party on three occasions.
At the other end of the field, John Oster did well to pick out Dean Shiels 20 yards from goal, but the former Hibernian forward dragged his shot wide.
Garry O'Connor saw a tame left-footed strike easily saved by Sullivan in the 40th minute and the Tykes striker was in pain moments later after injuring his hand in an aerial challenge.
O'Connor was able to continue after treatment, but Doncaster were forced into a change prior to the interval as Wilson limped off with a hamstring injury to be replaced by Irish midfielder Paul Keegan, who was making his Rovers debut.
The ineffective Trippier was withdrawn by Mark Robins at the break, with O'Brien coming on in his place.
Barnsley started the second half brightly and both Hugo Colace and O'Connor had efforts on goal before the latter shot narrowly wide from Jacob Butterfield's inviting left-wing cross.
The Tykes' pressure was duly rewarded as Haynes opened his account for the club.
Colace wasted a golden opportunity to double his side's advantage five minutes later as he shot wide following excellent work from O'Brien.
The miss was not to prove costly, however, as Haynes grabbed his second goal of the game to put Barnsley in control.
Foster was forced off with 20 minutes remaining following a heavy challenge from Sharp, who was booked. The centre-half became the fourth player to leave the field through injury, with Chambers and Kilgallon having followed Wilson in making premature exits.
Rovers toiled away in the closing stages but never looked like finding a way back into the game.
O'Brien almost added a spectacular third for Barnsley with six minutes remaining when his thunderous 30-yarder struck the side-netting.