Doan scored in his third straight game and the Coyotes withstood a late rally to beat the reeling New York Rangers 3-2 on Saturday night.
Sami Lepisto had his first career goal and Mikkel Boedker also scored for the Coyotes, who built a 3-0 lead in the first period. They have won three straight and six of eight to move three points ahead of Colorado for fourth place in the Western Conference.
"It was a game where we were in control early and the style that they play tends to make the game look a little bit ragged," Coyotes coach Dave Tippett said. "We had some opportunities in the second period but didn't put it away."
"We stayed with it and got rewarded at the end, just not enough," Rangers coach John Tortorella said. "We battled hard, we regrouped and we made a game out of it."
Gaborik came within inches of tying the game with 1:26 left, bouncing a short-handed attempt off the right post after a scramble in front.
"The rebound was flying through the air and I tried to bat it out of the air," Gaborik said. "That's the way it goes right now."
Doan put Phoenix ahead 1-0 at 6:05 of the first period, skating in from center ice and fighting through Michael Del Zotto's attempted poke check before sliding the puck off the inside of goalie Chad Johnson's right leg for his 17th goal.
"I thought I had the puck, but it bounced off of his chest," Del Zotto said. "Still, I can't let him beat me there."
Boedker, recalled from San Antonio of the American Hockey League on Friday, made it 2-0 just 42 seconds later when he took a pass from Robert Lang in the low slot, turned and scored on a backhand shot on his first shift.
"I don't know why I didn't put him on the ice sooner," Tippett said.
Boedker had two assists in 10 previous games with Phoenix this season.
"Obviously, you get disappointed when you get sent down, but there's nothing else to do but get back on my horse and keep working," Boedker said. "A lot of great players in this league have been down there so I'm not the first guy that has been disappointed."
The Coyotes made it 3-0 when Lepisto took advantage of a crowd in front of the Rangers net and rifled a wrist shot from the point past Johnson at 14:13.
"I saw it go by and I could hear his shot," said Johnson, making his fourth appearance of the season. "I just tried to go down and be as large as I possibly could. It was a tough goal."
Gaborik snapped the Rangers' 202-minute road scoreless streak with 10:18 remaining, taking a pass from Eric Christensen on the right doorstep and shooting into the open right side of the net.
Avery made it 3-2 with 8:50 to go, stealing a pass at center ice and beating Jason LaBarbera from the right faceoff circle.
"They came out a little bit harder and we kind of sat back and watched," said Vernon Fiddler, who assisted on Lepisto's goal. "We weren't doing the little things that got us the lead."
The game was played in front of 16,687, the Coyotes' third-largest crowd of the season. Phoenix was without Scottie Upshall, who sustained a lower-body injury in Thursday's win over Calgary. Lang's assist on Boedker's goal was the 700th of his career. The Rangers had not scored on the road since Dan Boyle's goal at St. Louis on Jan. 16. Taylor Pyatt added a pair of assists for the Coyotes. Before the game, Phoenix inducted former captain Teppo Numminen into the team's Ring of Honor. Numminen, who played 1,098 games for the franchise, is the fourth player so honored and the first to have played for the team since its 1996 move to Phoenix from Winnipeg.