Keith Yandle scored the deciding goal late in the first period and Mike Smith stopped 33 shots, as Phoenix squeaked by San Jose, 2-1, on Wednesday.
Michael Stone recorded the other score for the Coyotes, who won for the second time in their last six games.
"We came out, played hard and played to win," Coyotes head coach Dave Tippett said.
Brent Burns notched the lone score and Thomas Greiss made 30 saves for the Sharks, who have lost two of three.
With a regulation loss, San Jose remained tied with Los Angeles -- which lost to the Red Wings earlier on Wednesday -- for the fourth spot in the West. San Jose plays the Kings in both clubs' season finale on Saturday.
Yandle doubled the hosts' advantage late in a power play with 2:08 left in the period on a one-timer from the right point.
A Burns wrister halved San Jose's deficit with 3 1/2 minutes gone in the second, but that was all Smith allowed.
Greiss was pulled for an extra attacker in the final 90 seconds remaining, and Mikkel Boedker narrowly missed an empty-net tally moments later when his try from the left-wing boards skidded through the crease inches from the goal line.
As time ticked away, Smith attempted to clear the puck up the middle, but it never left the zone, and he was forced to make saves on Burns and Dan Boyle in rapid succession before the buzzer sounded.
"I liked the effort," Boyle said. "We had a lot of chances."
Stone's blast gave the Coyotes a 1-0 edge with just over eight minutes remaining in the first. Shane Doan won a battle along the left-wing boards and dished back to Radim Vrbata at the point. He, in turn, found Stone on the right wing for a successful slapper from the right circle.
San Jose won three of five in the season series, but Phoenix won its first home game against the Sharks since a 2-0 decision on March 29, 2012 ... Doan's two assists were his most in one game this year.