The home side had the perfect start to the game when they won a corner, and from Conor Hourihane's set piece defender Lewin Nyatanga rose highest in the penalty area to power a header past Sam Johnstone.
Doncaster almost hit back as Curtis Main and Kyle Bennett combined to release the latter through the middle of the Barnsely defence, but Ross Turnbull was on hand to make a good save to deny the midfielder.
Barnsley nearly doubled their lead when Leroy Lita pounced on a loose ball outside the area and volleyed an effort at goal which looked to be finding the top corner, but Johnstone palmed the ball away.
The visitors threatened again when Robinson raided forward to the edge of the box, and he curled a powerful effort at goal, but Turnbull made good save to tip his strike past the post.
Turnbull kept his side in the lead as he made another quality stop to deny Robinson after the striker had weaved his way into the box, while minutes later he was forced to tip a strike from Bennett over the bar.
After the break, Rovers got their equaliser when Richie Wellens drove forward into the box and picked out Robinson, who managed to turn past a defender and drill a low effort past Turnbull.
Doncaster nearly moved ahead in the match when Enda Stevens broke down the right flank and crossed into the box, and Main beat his man to the ball but could only poke his strike past the post.
The visitors had a chance to win the game late on when Robinson and James Coppinger linked up inside the box, and midfielder found Bennett in the box but he fired his effort straight at Turnbull, as both sides were forced to settle for a point apiece. body check tags ::