Matt Hendricks, David Perron and Ryan Nugent-Hopkins responded for the Oilers (15-32-6) who have now lost six in a row for the second time this season and have had five losing streaks go five games or longer.
The Oilers, who are just three points ahead of last-place Buffalo, only have two wins in their last 13 games.
The Coyotes started the scoring 14 minutes into the spirited first period as Antoine Vermette made a cross-ice pass to send Boedker in with some steam, beating Oilers goalie Ilya Bryzgalov with a well-placed wrist shot to the top corner. It was Boedker's 15th goal of the season.
Phoenix took a two-goal lead with three minutes left in the opening period after some quick passing allowed Martin Hanzal to put it in front to Vrbata and he rifled it home for a power-play goal.
Just over a minute later, it was 3-0 Phoenix, as some shoddy defensive play allowed the puck to squirt back toward the blue-line. Morris skated in and got all of his weight behind a shot that beat Bryzgalov to the glove side.
Mike Smith was as busy as Bryzgalov in the Phoenix net, as both goalies faced 15 shots apiece in the first period.
The Coyotes kept coming with another goal three minutes into the second period as a shot that was going wide was deftly tipped into Edmonton's net by Ribeiro.
Edmonton finally got on the board with seven minutes left in the second period as Hendricks redirected Ryan Jones's shot past Smith for his first goal in his fourth game as an Oiler since coming over in a trade with Nashville.
The Oilers made it a 4-2 game 1:50 into the third as Perron picked a puck up off the side boards and made a couple of nice moves to get past the Phoenix defenders before lifting a backhand shot top shelf past Smith. It was Perron's team-leading 19th goal of the season.
Edmonton then cut the lead to a single goal eight minutes into the third as Jordan Eberle drew the defence to him before sending a nice backhand pass to a trailing Nugent-Hopkins, who sent a quick shot into the Coyotes net.
The Oilers continued to press and had several good opportunities late in the game but couldn't get the equalizer.
Both teams return to action on Sunday as the Oilers play host to the Nashville Predators and the Coyotes travel to Vancouver to play the Canucks.
Notes: It was the fourth of five games between the two teams, with the Coyotes having won the first three, including a comeback for a 4-3 overtime win in Phoenix on New Year's Eve. The Coyotes entered the game with four straight wins over the Oilers, and having won nine of the last 11 encounters between the two teams overall. They had also won seven of their last eight in Edmonton… Oilers captain Andrew Ference left the game with a head injury and did not return…. Edmonton winger Nail Yakupov returned to the lineup after missing the last two games with a head injury. Fellow Russian Anton Belov also drew back into the lineup to take the place of veteran Nick Schultz... Oilers forward Ales Hemsky remained out with an ankle injury… Coyotes centre Martin Hanzal (lower body) and defenceman David Schlemko (upper body) were both back on the ice for Phoenix after missing Wednesday's game against Calgary.