Couture was hurt in the second period when he slammed into the boards awkwardly and limped off the ice. However, he returned before the end of the second and went on to score in overtime.
The Sharks expect Couture to be ready for Game 4 of the series Tuesday (10 p.m. ET, NBCSN, TSN, RDS).
Also sitting out practice was Martin Havlat, who aggravated a lower-body injury in Game 3 and will not play in Game 4.
Burish was ruled out for the second round prior to the start of the conference semifinals, but he appears to be ahead of schedule.
"He had a lot of energy and actually moved the puck fairly well," Sharks coach Todd McLellan told CSNBayArea.com. "Maybe he's closer than we originally thought. It's a good sign for us."
Burish is hoping a long series means he's able to return sometime in the second round.
"I'd like to get back,” Burish said. "If the doctors let me, I'd play tomorrow if I could. My goal is to get back in this series sometime. When that is, I don't know. It will be between us and the coaches and the doctors to see when that is. But I'll be ready whenever it is."
With Burish, Havlat and the suspended Raffi Torres out, McLellan had defenseman Jason Demers skate as a forward at practice Monday, and said using Demers up front is a possibility. Demers has been sidelined since April 18 with an ankle injury, but could be an option for Game 4.
"We were preparing in case we would like to use that option," McLellan said of shifting Demers to forward. "If we dress seven [defensemen], we may move somebody up to play some shifts. It's an option as [Demers] gets healthier, and time goes on."