Vesa Toskala stopped all 25 shots he faced in the last two periods after replacing Evgeni Nabokov, who left with a stiff neck after the first. Nabokov had 13 saves in the opening period.
Yanic Perreault scored late in the first period to give Phoenix a 1-0 lead.
Both teams squandered two-man advantages in the first period. Phoenix managed only two shots during their opportunity lasting 1:39, wasting valuable time while trying to make the perfect pass.
Just after the failed opportunity, the Coyotes' Donald MacLean appeared to score, but referee Mike Hasenfrantz immediately waived off the tally because MacLean kicked the puck crashing in from the slot.
The Sharks were then unable to score during their two-man opportunity for about 57 seconds after Phoenix was whistled for too many men while Patrick Fischer was off for tripping.
However, Perreault scored at 19:09 as he converted a centring pass from Oleg Saprykin and redirected the puck past Nabokov.
Bernier tied the score with his fifth goal of the season, deflecting a pass from Scott Hannan at 3:58 of the second period.
Marleau's drilled a slap shot over Joseph's right shoulder at 10:34 for his 11th of the season.
Notes: Perreault's goal was his first with Phoenix after signing a one-year deal with the Coyotes on October 30. ... Both teams were 0-for-4 on the power play. ... The Coyotes Dave Scatchard left the game in the third period with a leg injury, and did not return.