The win allowed San Jose to keep pace with Dallas and Minnesota and remain tied for fifth place in the Western Conference.
"We have 11 games left and our focus is where it needs to be," Sharks coach Ron Wilson said.
Cheechoo also had an assist, and Milan Michalek, the third man on the Sharks' top line, helped set up each of his linemates' three goals.
"We have so many good offensive players with good offensive instincts," Thornton said. "When you give the puck up we're so fast and so strong we're going to jump on you quick and be able to score a couple of goals."
Cheechoo proved Thornton's point, giving the Sharks a 1-0 lead 78 seconds in when he swept a long rebound just inside the left post for his 24th goal.
He added his second at 4:10 of the middle period on a backhand attempt after the puck bounced back to him in the low slow after a scrum in front.
The Sharks never looked back.
"Joe made a great pass and got it out there," Cheechoo said. "The goalie was overplaying me and I had an opening low on the glove side."
Bill Guerin added his team-leading 32nd goal, and Matt Carle scored his 11th for the Sharks, who won for the fifth time in six games.
"We roll four lines all night, roll six on defense and have great goaltending," Thornton said. "We have so much depth and we're really confident right now. We're playing great hockey right now."
Travis Roche scored a power-play goal for the Coyotes, who have lost six of seven and 13 of 16 (3-12-1).
"Some times when a team is in the playoffs they can take these teams lightly," Sharks defenseman Kyle McLaren said. "These are important points for us to stay in fifth and to see if we can catch Anaheim. We didn't want to give these points away so I like the way we are starting."
Though technically out of the playoff hunt for weeks, Phoenix officially was eliminated from the race with the loss.
"Realistically, regardless of what happened tonight, we knew the situation," Coyotes coach Wayne Gretzky said.
Guerin extended San Jose's lead to 3-0 at 7:33 of the second with a hard wrist shot from the left circle.
The Sharks have outscored opponents 15-2 in the second period over their last 11 games.
Roche cut the lead to 3-1 at 3:48 of the third period, taking a pass from Owen Nolan along the goal line and sliding the puck past Evgeni Nabokov from just outside the crease.
Thornton put the Sharks in front 4-1 when he took a pass from Cheechoo to start a 2-on-1 break. He beat Mikael Tellqvist on a backhand shot from just inside the right circle.
Carle capped the scoring with a power-play goal with 10:21 remaining.
"You have to play a game where you are willing to win 1-0, where you are willing to be solid in your own zone for the entire game," Coyotes captain Shane Doan said. "You can't have any mental lapses and if you do, the Sharks are going to capitalize every chance they get."
Notes: Cheechoo has 12 goals and seven assists in 24 career games against the Coyotes. ... San Jose outshot Phoenix 15-2 in the first five minutes of the first two periods, but were outshot 15-4 the other 30 minutes. ... The Sharks have won five of the seven meetings this season. ... Thornton raised his point total to 93. Phoenix's lineup, including Tellqvist, entered the game with a combined 116 points.
|Jonathan Cheechoo (24) ASST: Joe Thornton (73), Milan Michalek (30)|
1 - 0 SJS
|Jonathan Cheechoo (25) ASST: Milan Michalek (31), Joe Thornton (74)|
2 - 0 SJS
|Bill Guerin (32) ASST: Patrick Marleau (38), Mark Bell (8)|
3 - 0 SJS
|PPG - Travis Roche (6) ASST: Owen Nolan (20), Bill Thomas (4)|
3 - 1 SJS
|Joe Thornton (18) ASST: Jonathan Cheechoo (28), Kyle McLaren (10)|
4 - 1 SJS
|PPG - Matthew Carle (11) ASST: Milan Michalek (32), Joe Thornton (75)|
5 - 1 SJS
|Steve Reinprecht Hooking against Bill Guerin|
|Jonathan Cheechoo Holding against Jeff Taffe|
|Michael Zigomanis Hooking against Jonathan Cheechoo|
|Kyle McLaren Hooking against Daniel Carcillo|
|Kyle McLaren Roughing against Daniel Carcillo|
|Daniel Carcillo Hi-sticking|