Graves, who spent the previous 10 seasons with the Rangers and helped them win their first Stanley Cup since 1940 in 1994, was traded to San Jose during the offseason.
Always a fan favorite, Graves was greeted with a rousing ovation during a pregame ceremony and received a smattering of applause when his name was announced on Damphousse's first goal of the night.
With 38 seconds to go in the second period, San Jose regained a two-goal lead with its second power-play goal of the game. Damphousse collected a rebound of Graves' shot from the left faceoff circle and buried it on the right side.
San Jose built a 4-1 lead 2:05 into the third period, when Patrick Marleau spun away from the Rangers defense at the right boards and fired a shot over the shoulder of rookie goaltender Dan Blackburn.
Damphousse scored his second goal of the night on a shorthanded breakaway with 3:04 remaining to secure the win.
San Jose opened the scoring 3:40 into the first period when Mike Ricci sent a pass through the crease to Scott Thornton at the left side of the net. Thornton deflected the puck over Blackburn.
The Sharks scored again six minutes later. Selanne set up the play from behind the net, feeding the puck to the top of the crease for Graves, who fanned on the one-timer. But the puck trickled back to defenseman Brad Stuart, who fired it through traffic for a 2-0 lead.
The Rangers gained some momentum late in the first period and early in the third but struggled to get on the board.
Defenseman Vladimir Malakhov nearly cut New York's deficit to one with 48 seconds remaining in the first when his shot from the left faceoff circle hit the right goalpost and slid along the goal line before Nabokov covered up.
The Rangers failed to convert on a 54-second 5-on-3 to open the second period. Nabokov came up with three key saves, including two point-blank one-timers by Radek Dvorak and another by Eric Lindros at the left side of the net.
Rangers defenseman Dave Karpa left the game during the first period with a separated left shoulder and did not return.