Georges Laraque, who left Edmonton to sign a free-agent deal with Phoenix last summer, scored his first goal of the season for the Coyotes, who snapped a four-game losing streak. Zbynek Michalek, Ladislav Nagy, Oleg Saprykin, Owen Nolan and Donald MacLean also scored for Phoenix.
Fernando Pisani scored his first goal of the season and Petr Sykora added a goal for Edmonton, which lost for the second time in two nights.
LeNeveu was recalled Thursday to replace Mike Morrison, who was assigned to AHL San Antonio after clearing waivers. Morrison had a 6.14 goals-against average in four games.
LeNeveu, who played 15 games with Phoenix last season, earned his fourth career victory.
Phoenix had lost its last four games by a combined score of 19-3. The Coyotes came into the game with four points, fewest in the Western Conference.
With Edmonton's Marty Reasoner serving a hooking penalty, the Coyotes went ahead 1-0 on Michalek's second goal of the season at 5:08 of the first period.
It took only 1:21 for the Oilers to tie it at 1-1. After LeNeveu stopped winger Ales Hemsky on a breakaway, Pisani beat LeNeveu with a wrist shot over the right shoulder. It was the first point in 10 games for Pisani, who was rewarded with a US$10-million, four-year contract after scoring 14 goals in 24 playoff games last spring.
The Coyotes made it 2-1 on Nagy's third goal of the season at 11:07 of the first period.
Then Laraque, not known as a scorer, created his own chance by shouldering Reasoner away from the puck, stickhandling along the goal-line and backhanding a shot over Markkanen.
Edmonton coach Craig MacTavish replaced Markkanen with Dwayne Roloson, who gave up six goals in a 6-2 loss at Anaheim Wednesday night.
Notes: Coyotes captain RW Shane Doan (back) was scratched. . . . Sykora leads the NHL with three game-winning goals. . . . Markkanen had allowed one goal in his only previous start, a 2-1 victory over Vancouver Oct. 17. . . . Nils Lofgren sang the national anthem. The Coyotes are 6-0 when Lofgren sings the anthem.