Richards was the second shooter for Dallas and he deked to the forehand before putting it behind Antti Niemi. Ryane Clowe was the third skater for San Jose and Andrew Raycroft made a right pad save on the stuff attempt for the win.
Clowe and Derek Joslin each scored for the Sharks, who came into the game having won three of four. Niemi made 29 saves in the loss.
Dallas grabbed a 1-0 lead with the only goal of the first period at the 6:17 mark. Ribeiro caught up with the puck behind the right side of the net and threw it out front for a wide-open Benn, who wristed it home.
The Sharks tied the game 6:56 into the second on Joslin's first NHL goal and took a 2-1 lead two minutes later thanks to Clowe's ninth goal of the season.
The Stars tied the game on the power play late in the second when Stephane Robidas blasted a shot from the left point that Ribeiro deflected past Niemi.
The third period and overtime saw Raycroft stop 15 shots and Niemi make 10 to force a shootout.
San Jose hits the road for the next three games starting in Nashville on Wednesday...Dallas hosts San Jose on Thursday...Dallas has taken both games against San Jose this season and six of the last eight...Dallas went 1-for-3 on the power play and San Jose failed on its only chance.