Kyle Okposo had two goals in New York's fourth consecutive victory. The Islanders (18-22-7) also have won seven straight road games.
The Islanders rallied past the Stars after trailing 2-0 after one period for the second time in a week. Taveras has four goals and three assists in the two games. Thomas Vanek has four assists and Okposo has the two goals.
This time, New York scored three goals in the final 4:16.
"We're competing. We're defending a little better," Islanders coach Jack Capuano said of the team's recent success. "Playing more within the team concept. I think when you can utilize your four lines that we do, a lot of guys the minutes are distributed."
Dallas (20-18-7) has lost six in a row for the first time since March 2011.
"When our goaltenders play well, we give ourselves a chance," Capuano said. "(Injured goalie Evgeni) Nabokov was playing well and the last few games Kevin has played well for us too."
The Stars had 11 giveaways in the game to only two by New York.
"They came at us pretty good for the last 40 minutes," Whitney said. "It was a combination of them playing a little better than they did in the first and us turning the pucks over at the wrong time and against the wrong line."
Okposo scored in the second, and tied it at 15:44 of the third with a drive from the top of the right faceoff circle.
"We knew we could turn it around," Okposo said. "I thought still in the second period we came out a little bit slow but started to tilt the ice."
For the winning goal, Tavares got a cross-ice pass from Calvin de Haan and beat Dan Ellis from the right faceoff circle for his 21st goal of the season, including four against the Stars. Ellis scrambled to get back across the goal, and tried in vain to glove the puck before it went into the short side of the net.
"It's just great awareness by Cal and Thomas, two great plays really to set it up," Tavares said. "I had the easy part, to put it in. Just kind of go to the net hard, find some open space and happy the puck came to me."
Ellis stopped 27 shots.
"Dan made probably three or four great saves to keep the score where it was at," Stars coach Lindy Ruff said. "He made the saves that could have allowed us to win the game, even get a point out of the game."
The Stars' first goal was at 11:45 of the first period. Vernon Fiddler hustled in to pick up the puck against the back boards, and pushed it across to Alex Chiasson. He passed to Whitney skating into the left circle, and his shot went in past Poulin's left leg.
Gonchar then intercepted a pass inside the blue line, skated to the top of the right circle and fired a shot inside the left post at 18:12. It was the first goal of Gonchar's 19th NHL season.
The Islanders began their comeback in the second period. They nearly scored 9 minutes in, but Ellis stopped Colin McDonald's tip from in front of the net.
Okposo then broke through for New York at 10:47 of the second, scoring from low in the right circle. Assists went to Vanek and Tavares.
In last Monday's game, Tavares tied a career high with five points. Vanek added two assists, but Okposo missed the game because of the birth of his first child. The line totaled three goals and three assists Sunday. ... Vanek has at least one point in 11 of his last 12 games, with a total of 17 points. ... New York defenseman Travis Hamonic did not play in the third period because he was sick. ... The Stars' six consecutive losses all have been against Eastern Conference teams.