Heatley, who was acquired in a trade from Ottawa on Sept. 12 in a multiplayer deal that sent wingers Milan Michalek and Jonathan Cheechoo to the Senators, started for San Jose and played sparingly in each period but did not score.
"It was good to get it over with," Heatley said. "I felt pretty good. It was nice to see Patty put it away tonight."
Marleau's goal with 3:02 remaining in the third period tied the game before he made the game-winner 2:29 into overtime.
Coyotes coach Wayne Gretzky, whose $8.5 million contract for 2009-10 is part of a bankruptcy dispute being adjudicated in a Phoenix court, missed his fifth straight game.
Heatley, who practiced with his new teammates for the first time on Friday, lost a faceoff to Phoenix center Vernon Fiddler early in the first period then missed on a centering pass in front of the net that sailed long and hit the glass in the far corner. Less than a minute later, Clowe took a short dump-in pass from Joe Pavelski and scored to put the Sharks up 1-0.
Heatley also missed an assist late in the first period when Phoenix goalie Ilya Bryzgalov blocked Setoguchi's shot.
"It'll take a little getting used to, the roots of what (coach Todd McLellan) wants, and getting used to Joe (Thornton) and Seto," Heatley said.
The 6-foot-4, 221-pound Heatley is a five-time All-Star and has the Senators' records for goals (50) and points (105) in a season. He has 260 goals and 283 assists in 507 regular games during his career but is coming off his lowest point total in four seasons.
Setoguchi, who was second on the Sharks with a career-high 31 goals in 2008, scored from the right faceoff circle 38 seconds into the second period. McGinn followed with his goal just over a minute later to make it 3-0.
Phoenix didn't show much offense early but got going when Meyer scored in the second period then assisted on Justin Bernhardt's goal 6:01 into the third. That began a flurry of scoring for the Coyotes, as Michalek and Turris scored within a minute of each other to give Phoenix a 4-3 lead.
San Jose defenseman Nick Petrecki, who is trying to win one of the last defensive spots on the Sharks' roster, and Fiddler were both kicked out of the game for fighting less than six minutes into the first period.