Gavrikov, who was in the slot, backhanded a rebound into the net after Casey DeSmith made the initial left-pad save on Artemi Panarin.
Will Cuylle scored the tying goal with 2:13 remaining in regulation. Igor Shesterkin finished with 23 saves and Carson Soucy also scored for the Rangers (14-12-2).
DeSmith made 40 saves, but the Stars had their four-game win streak end. Their point streak, however, remains alive as they are 5-0-2 in their past seven games. Dallas (17-5-5) is also 7-0-4 on the road since Oct. 26 and 9-1-4 this season.
Mikko Rantanen scored in the third period and Kyle Capobianco’s goal in the first period was his first in more than two-and-a-half years.
Soucy gave New York a 1-0 lead at 6:51 of the first period. Conor Sheary played the puck up the right-wing wall to Soucy, who moved it to the middle for Noah Laba. He got alone on DeSmith and his shot squeaked through the goalie. Soucy put it in off the goal line.
Capobianco got it back at 9:04, scoring his first NHL goal since March 4, 2023 to make it 1-1.
He had his first shot blocked by Braden Schneider. Gavrikov tried to clear the puck out of the slot, but it instead went to Capobianco. He kept his second shot low, skimming the puck off the ice and getting it through Shesterkin’s five-hole.
Rantanen gave Dallas the 2-1 lead at 9:32 of the third period, scoring off a 2-on-1 rush with Wyatt Johnston, who started the play by stealing the puck from J.T. Miller near the blue line in Dallas’ defensive zone.
Cuylle made it 2-2 at 17:47. He got the puck off a rebound on the left side, twirled around and scored with a shot that went in off DeSmith.
Stars forward Tyler Seguin did not return after leaving with a lower-body injury at 1:44 of the first period.