Marcus Johansson scored at 7:59 of the first period to give the Sabres a 1-0 lead and Skinner made it 2-0 44 seconds later. Wayne Simmonds had an assist on Skinner's goal and needs one point for 500 in his NHL career.
"After those two goals went in we got the urgency we needed," Oesterle said.
Oesterle cut it to 2-1 at 2:20 of the second for the first of five consecutive Coyotes goals. Phil Kessel tied it at 2-2 at 3:13.
"We lost our game for five or six minutes there, and it was hard to get it back," Sabres coach Ralph Krueger said.
Keller scored the third goal in a span of 5:10 to make it 3-2 at 7:30 and extended the lead to 4-2 at 13:59 of the third. Ekman-Larsson scored shorthanded into an empty net at 19:40 for the 5-2 final.
"I felt pretty good," Keller said. "Even though we were down 2-0 I still felt good about our game."
Keller, moved to the Coyotes No. 1 line with Taylor Hall and Christian Dvorak after the first period, has four goals in his past three games after having one goal in his previous 20.
"I could tell he had it going," Coyotes coach Rick Tocchet said. "The last few weeks he has been one of our better forwards. He's out on the ice early before practice and I know he wants to finish strong."
The win was Tocchet's 100th as Coyotes coach (100-103-28). He is 153-172-54 with Arizona and the Tampa Bay Lightning.
"We've got to go to Vancouver (on Wednesday) and do the same thing. You just can't do it on whatever the day is, you've got to do it every night, and that's the key now more than ever," Tocchet said.
Sabres forward Victor Olofsson left with lower-body injury 3:30 into the second period. He missed 15 games with an ankle injury before returning Feb. 13.
"Obviously he's a big part of the team, and you don't like to see it when guys go down," Skinner said.
