DiPietro made 13 saves before leaving because of a lower-body injury with the Islanders up 4-1 in the second period. He was credited with the win.
After the game, DiPietro described his injury as a "little tweak" and wasn't sure how long he would be out -- if at all. He will be re-examined Tuesday. He hurt himself sliding across the crease to try to stop a shot from Jarome Iginla, which whistled off the crossbar.
"I don't know if a man's body is supposed to be contorted in those kind of positions," said DiPietro, who was facing a barrage of pressure during a Flames power play at the time. "I felt a twinge and hopefully it's nothing serious."
Lawson, recalled from Bridgeport of the American Hockey League after the Islanders traded Dwayne Roloson to Tampa Bay on Saturday, allowed just a single goal on 29 shots.
Although he didn't get the win, it sure felt like a victory for Lawson. He lost in a shootout in his only NHL start against Phoenix on Dec. 18.
"It feels good to get a win and get a few games under my belt now," the 27-year-old goalie said. "It's a dream come true. I just want to keep rolling with it and prove myself now."
Islanders interim coach Jack Capuano knows Lawson well, having coached him in the minors.
"I know what a competitor he is and he came in on a power play, too. Pretty rough go for it there but he accepted the challenge," Capuano said. "I thought he was square to the puck, played the rebounds pretty well, and he battled for us tonight."
David Moss scored both goals for Calgary, which got 21 saves from second-string netminder Henrik Karlsson. The Flames had their four-game winning streak snapped.
"At the start of the game we weren't assertive. We didn't respect our opponent enough," coach Brent Sutter said. "We tried to play half a game tonight and it didn't work for us."
The Islanders raced out to a 3-1 lead in the first period. Tavares scored on the power play at 3:37 before Moulson doubled the lead at 8:29.
Moss got one back for Calgary just more than three minutes later, but Tavares scored his second of the night and third point of the period at 13:25.
"A good all-around game for us," Tavares said. "Great for Lawson to get in there and do his thing, coming in cold. Everyone did their role and we handled the lead well and the pressure when we needed to."
Moulson made it 4-1 at 3:06 of the second, but Moss again cut the New York lead with his second at 13:22. Moss had a great chance for a hat trick late in the second period, but Lawson jabbed out his leg to rob the Flames' forward from 15 feet out.
Grabner added an empty-net goal with just more than a minute remaining. New York has won the first two games on its five-game road trip, which continues Thursday night in Edmonton.
"We know we didn't deserve to win that game from the way we started. We got outworked in the first period, beat to pucks, outhustled, made foolish mistakes," Iginla said. "It's not a case of taking them lightly. We know they had beat Detroit and were 6-1-1 coming in."
The last Calgary backup goalie to win at home was Curtis McElhinney against Edmonton on Dec. 31, 2009. Dating to the 2005-06 season, Calgary has gotten just five victories at home from Miikka Kiprusoff's backups. ... It was only the second game for DiPietro in the building in which he was taken first overall in the 2000 NHL Entry Draft. ... New York RW Blake Comeau (back spasms) did not play.