"When you pay attention to details and demand it from each other it's contagious," Sullivan said. "That's what winning teams have and that's what we need to get back."
Doan, who has four goals and five assists in his last seven games, scored with 1:08 left in regulation to lift Phoenix to a 3-3 tie with Boston. The Coyotes got their 12th point in overtime games this season.
"We worked hard for the full game -- not always the smartest, but we did work hard," Doan said.
Glenn Murray scored his eighth goal of the season 16 seconds into the third period to give the Bruins a 3-2 lead.
Travis Green scored a goal and added an assist for Boston, which has a 2-3-4 record in overtime games this season. Patrice Bergeron also scored for the Bruins.
Tyson Nash scored his second goal of the season and had an assist for the Coyotes, who have only two wins on the road this year. Mike Sillinger added a short-handed goal for Phoenix.
Sean Burke (7-7-3) made 37 saves for Phoenix, including six in a two-minute span in the second period when Boston had a two-man advantage.
"Sean played well. That's the type of game we've come to be accustomed to," Coyotes coach Bob Francis said.
Felix Potvin stopped 28 shots for Boston.
Green opened the scoring 4:54 into the first period on a backhander from just outside the crease.
But Phoenix tied the score at 1-all with 9 seconds left in the period on Sillinger's short-handed goal from the right faceoff circle.
Bergeron gave the Bruins a 2-1 advantage 5:58 into the second period on wrist shot from the right circle.
The Coyotes tied the game when Chris Gratton one-timed a shot past Potvin with 1:02 remaining in the middle period.
The Bruins were 0-5 and the Coyotes 0-2 in power-play opportunities.
|Travis Green (2) ASST: Hal Gill (4)|
1 - 0 BOS
|SHG - Mike Sillinger (2) ASST: Tyson Nash (2)|
1 - 1 Tie
|Patrice Bergeron (6) ASST: Travis Green (1)|
2 - 1 BOS
|Chris Gratton (3) ASST: Tyson Nash (3), Ossi Vaananen (3)|
2 - 2 Tie
|Glen Murray (8) ASST: Joe Thornton (20)|
3 - 2 BOS
|Shane Doan (9) ASST: Mike Sillinger (3), Paul Mara (12)|
3 - 3 Tie
|Power Play %||0.0%||0.0%|
|% on Road||0.0%||0.0%|
|% at Home||0.0%||0.0%|
|Tyson Nash Hooking|
|Paul Mara Hooking|
|Mike Sillinger Tripping|
|Tyson Nash Slashing|
|Brian Rolston Hi-sticking|
|Shane Doan Roughing|
|Travis Green Holding the stick|