Ekman-Larsson gave the Coyotes a 2-1 lead with a power-play goal with 49 seconds left in the second period. He got a pass from Domi near the blue line in the middle of the zone and shot past Talbot's glove.
Benning scored at 14:25 of the third period to tie it 2-2 on a shot through traffic from the right point.
"We needed a desperate effort tonight," Talbot said. "We can't afford to keep giving up points, especially at home. We need this to be a tough building to play in. [Benning] got us a big goal at the end of the third, and anytime we go into 3-on-3, I like our chances. It's just a matter of giving our guys a chance to get there."
Arizona outshot Edmonton 4-1 in overtime, and Coyotes forwards Clayton Keller (1:02) and Christian Dvorak (3:32) each hit the crossbar.
"We had two breakaways and two posts and a missed shot [in overtime]," Arizona coach Rick Tocchet said. "We had a lot of chances tonight and we deserved to win that game, and the Oilers capitalized on the amount of chances they had, but we had a lot of chances tonight."
Nugent-Hopkins set up his breakaway by tipping the puck past Ekman-Larsson at the Edmonton blue line with 45 seconds remaining.
"I guess you could call us lucky in overtime because we gave up four or five chances before we got our first," coach Todd McLellan said.