Acquired from Toronto as part of the Owen Nolan trade, McCauley had a pair of assists in his first four games as a Shark before forging a 2-2 tie with a power-play goal with 5:14 remaining in the second period.
McCauley, who had six goals in 64 games with the Maple Leafs, made a nice pass to set up Damphousse's 417th NHL goal and fifth game-winner of the season.
After taking control of the puck along the right boards in the neutral zone, his lead pass connected with Damphousse, who skated to the right faceoff circle and snapped a backhander over the left shoulder of goaltender Roman Turek for his 20th goal.
The Sharks wasted leads twice during the losing streak and squandered a two-goal lead in a 4-3 loss to Calgary two weeks ago. They almost did it again.
They needed several big stops by Vesa Toskala, who had not played in the NHL in nearly five months. Among his 32 saves were a pad stop on Jarome Iginla's penalty shot at 6:23 of the third period and a glove stop on defenseman Robyn Regehr's point shot with just under six minutes to play.