Lundqvist, who also stopped 29 in a win over Buffalo on Saturday, is 2-0 since signing a six-year contract extension with New York.
Jonathan Cheechoo had the lone goal for the Sharks, who have the fewest road losses in the NHL (17-6-3). San Jose is 4-18-3-0 against New York and hasn't beaten the Rangers since Oct. 22, 2001.
Evgeni Nabokov stopped 30 shots in starting for the 57th time in San Jose's 58 games this season.
The Sharks began an eight-game road trip, that continues Monday on Long Island, with their first visit to Madison Square Garden since Dec. 16, 2002.
New York went ahead 2-1, taking advantage against the NHL's best road penalty-killers and second best overall.
After giving up a scoring chance to San Jose forward Milan Michalek, the Rangers took control of the power play. Scott Gomez raced the puck up left wing and hit the brakes near the boards. He sent a cross-ice pass to Drury, who wound up for a slap shot that beat Nabokov inside the right post at 5:44.
New York received the advantage when Patrick Rissmiller put the puck over the glass in the San Jose zone. It was only the 11th power-play goal allowed by the Sharks on the road in 105 chances, the best percentage in the NHL. San Jose is second overall in penalty-killing, giving up 32 goals.
Callahan tied it 8 seconds after the Rangers' first power play expired.
One day after taking a 1-0 lead against Buffalo 10 seconds in and scoring four times in the first period, the Rangers settled for a tie through 20 minutes Sunday.
Drury chipped a pass from behind the right post behind him to Callahan, who quickly put a shot past Nabokov with 8:26 left.
The Sharks grabbed a 1-0 lead 3:31 in when Cheechoo's scored his 15th.
Cheechoo stood in front as Joe Thornton worked behind the net. He swung a pass that Cheechoo pinballed in off Rangers defenseman Marek Malik and Lundqvist.
The assist gave Thornton 500 in the NHL.
