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 to keep pace with Dallas and Minnesota and remain in sixth place in the Western Conference.
Cheechoo also had an assist, and Milan Michalek set up three goals for the Sharks.
Travis Roche scored a power-play goal for the Coyotes, who have lost six of seven and 13 of 16 (3-12-1).
Cheechoo gave the Sharks a 1-0 lead 78 seconds into the game when he swept a long rebound just inside the left post for his 24th goal. He made it 2-0 at 4:10 of the second on a backhand attempt after the puck bounced back to him in the low slot after a scrum in front.
Guerin extended San Jose's lead 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.
Notes: Cheechoo has 12 goals and seven assists in 24 career games against the Coyotes. ... 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.