At 12:59 of the first period, San Jose's Logan Couture pushed the puck past Elliott for a power-play goal that gave the Sharks a 3-0 lead.
There was a jumble of bodies in front of the net on the play. Elliott went down to block the shot, and the puck squirted past him.
After Blues trainers came out, Elliott left the ice and went to the locker room.
Jake Allen replaced Elliot and finished with 15 saves. The Blues activated Allen from injured reserve Sunday.
Allen sustained a lower-body injury during the team's game Jan. 8 against Anaheim and had missed 17 games.
"I haven't played in a month and a half," Allen said. "I got my feet wet. We got too far behind the eight ball to catch up."
The Associated Press contributed to this report.