Rochdale had taken the lead against the run of play on the half hour when a clearance by keeper Matthew Gilks was headed on by Paul Tait. With the home defence sleeping Grant Holt ran on to lash the ball past Willy Gueret in the home goal for his 22nd strike of the season.
Six minutes later home fans were stunned as Swansea's talisman Lee Trundle was shown a red card after a two-footed lunge on Dale's Jamie Clarke.
Straight from the restart referee Parks showed the red card again, this time to Rochdale's Tait who appeared to lash out at Kevin McLeod .
The match settled down a little after the dismissals with Swansea doing most of the attacking but, apart from a couple of strikes by the impressive Kristian O'Leary and Paul Connor, they failed to open up the visitors' defence.
Connor, who was playing his former club, led the Swansea line well but without Trundle there was a lack of craft and guile.
The second half was an open affair with Swansea levelling within a minute of the restart. The ball was walked out to skipper Andy Gurney wide on the right and he drove in a shot across the diving Gilks and inside the far post.
The Swans were gifted the lead six minutes later when Holt headed a McLeod corner into his own net.
Dale upped the tempo as the match drew to a close and they should have scored in the 80th minute but Gueret flung himself to his left to claw away a close range header by Gary Jones.
However they were not to be denied and in the final minute poor defending allowed Rickie Lambert to tap home the equalizer from close range.