It was end-to-end action and both sides had chances to secure all three points but a draw was a fair result and the point lifts the Swans back into the play-off position.
The Swans made two changes from the side that beat Port Vale with skipper Darren Pratley returning in midfield and Willy Gueret regaining his place between the posts.
The Robins had Steve Brooker after being absent for two months with a knee injury.
The visitors should have taken a fourth minute lead when a deep cross was headed back into the danger area, but Brooker nodded over the bar from two yards out.
The Swans hit back and Andy Robinson sent a free-kick against the side of the upright, before forcing Adriano Basso to go full-length to gather a crisp shot that went through a crowd of players.
The Robins opened up the Swansea defence in the 11th minute but Phil Jevons slid his shot wide of the far post.
Back came the Swans and Alan Tate beat Basso to the ball, but Jamie McCombe raced back to hack off the line.
McCombe almost diverted a Leon Britton shot into his own net in the 20th minute, but with Basso wrong-footed, it struck the base of an upright and went behind for an unproductive corner.
Midway through the half Robinson brought another fine save from Basso, who again had to be alert to push behind Lee Trundle's close-range shot from the corner.
The half finished with both sides continuing their promising build-up play but neither being able to finish it off.
The opening chance of the second half fell to Trundle, but his snap shot on the turn went straight to Basso.
The Swans pinned the Robins back in their own half and Robinson struck a free-kick on to the top of the crossbar with Basso beaten, before drilling a shot that the overworked keeper just managed to palm behind for a fruitless corner.
Ade Akinfenwa came on for the ineffective Rory Fallon to ruffle up the visitors' defence, but they held out for a thoroughly entertaining draw.