The Oilers, playing in vintage orange and blue jerseys from the team's 1980 Stanley Cup years, mustered just two shots in the first period compared with 10 for the Coyotes.
Fans cheered when the announcer sounded the last minute of play in each period and booed the home town team off the ice.
"Absolutely we deserved it," Oilers captain Jason Smith said. "We didn't come with the work ethic that we need."
Angry fans chanted "Smytty! Smytty! Smytty!"
"Let's go Islanders!" shouted another, referring to Smyth's new team.
Coyote forward Jeremy Roenick said the Oilers seemed to have their minds somewhere else.
"You could tell their team was a little flat with everything that was going on with Mess. That took a little wind out of their sails," Roenick said. "And then when Ryan got traded, that's a gut-wrencher. We definitely saw that their eyes were wide open by that."
Coyote coach Wayne Gretzky, who knows all about being surprisingly dealt away by the Oilers, added: "It was an emotional day and they have emotional fans. I'm sure this wasn't an easy game to play."
Phoenix opened the scoring with just over six minutes left in the first period when the Oilers failed to clear the zone while shorthanded. Coyotes defenseman Derek Morris dished the puck to Owen Nolan in the slot, who fired a shot past Oilers goalie Dwayne Roloson for his 15th goal.
Phoenix extended the lead in the second on the power play, when Morris' point shot deflected to Yanick Lehoux at the side of the net. He fired the puck past Roloson for his first goal of the year.
Steven Reinprecht made it 3-0 minutes later when he turned Oilers defensemen Jan Hejda inside out before backhanding the puck through the goalie's pads. The boos rained down. By the middle of the third, a quarter of the fans had gone home.
The 16,839 fans, who rattled the girders with cheers as Messier skated around with the Stanley Cup in the pre-game ceremony, seemed to be spent as well. They made little noise when highlights of Messier goals were shown on the JumboTron during breaks in the action.
Edmonton is now 2-2 against the Coyotes and its playoff hopes are fading fast. The Oilers were nine points back of a playoff spot heading into play Tuesday night.
- Oilers defenseman Ladislav Smid was a scratch after taking a knee in the thigh in a game against the Minnesota Wild on Sunday.
- Oilers defenseman Dan Syvret made his first NHL appearance of the year after being called up from the American Hockey League, but was in the penalty box for Phoenix's first goal.