Alan Tate had given the Swans the lead in the 43rd minute, but substitute Chris Greenacre slotted in from an acute angle to give his side a deserved point.
The Swans showed one change from a side beaten by Millwall with Dennis Lawrence coming into the back line.
Rovers were on the back foot for the opening ten minutes but the Swans were unable to carve out any openings until Thomas Butler slipped a pass inside to Jason Scotland, but Danny Coyne saved at the second attempt.
Scotland had another shooting chance after working his way through in the 15th minute, but once again Coyne came out to smother.
A free-kick by Rovers skipper Paul McLaren had Dorus de Vries diving to push behind for a corner, but it was an isolated attack by the visitors.
Two minutes before the interval a Ferrie Bodde corner was only partially cleared and Tate lashed the ball into the net to give his side the lead.
They had a lucky escape in the 48th minute when Shane Sherriff went through a couple of half-hearted tackles but he fired wide when well placed.
Midway through the half Andy Robinson was brought down just outside the area, but his free-kick was too high and rippled the top of the net.
Guillem Bauza replaced Scotland in the 73rd minute and tested Coyne with a fierce drive that had the former Wales international leaping to his left to save with an outstretched hand.
With injury time being played, a cross from Calvin Zola was turned into the net by Greenacre and Rovers had salvaged a deserved draw.