The Scottish international midfielder stroked home his 18th goal of the campaign in the second minute of added time to deny battling Barnsley a place in the record books.
Barnsley, who had beaten Albion 3-1 at Oakwell last September, had been on course to become the only side this season to do the double over Albion when Hugo Colace gave them a 59th minute lead.
But a late Albion assault earned them the goal their play had warranted with Dorrans converting a Roman Bednar cross.
Albion, whose 91 point total this season is a club record, had the majority of the chances, but some poor finishing and smart saves from their former goalkeeper Luke Steele looked set to cost them before Dorrans struck.
Barnsley, who were led into action by the former Albion skipper Darren Moore, should have broken the deadlock after just three minutes following good work by Jacob Butterfield.
His neat pass picked out Martin Devaney but he pulled his close range shot wide when he was faced with only Scott Carson to beat.
That was as good as it got for Barnsley in a low key first-half as Albion carried the greater threat without any end product.
Jonas Olsson headed a corner from Graham Dorrans over the bar and Chris Brunt and Bednar were off target with shots when well-placed.
Brunt was also denied by Steele in the 34th minute before the Northern Ireland international winger wasted the best chance of the opening period four minutes later.
He was picked out at the far post by Robert Koren but somehow conspired to bundle his shot wide from inside the six yard box.
Bednar then blazed over the bar when he should have done better after being let in by a mistake by Ryan Shotton.
That was a costly miss as Colace struck just four minutes later when he converted a Butterfield free-kick from six yards.
Steele then denied Koren and Ishmael Miller before Dorrans finally broke his resistance with a low 12-yard drive as Barnsley were denied their first win in 10 games.