Phoenix jumped ahead of Columbus and Edmonton into ninth place in the Western Conference, two points behind St. Louis and three behind seventh-place Detroit.
Smith hadn't played since sustaining an upper body injury on March 21 when he was run over by Vancouver defenceman Alexander Edler.
Against the hapless Avalanche, who are 4-13-1 in their past 18 games, Smith rarely was tested. He posted his 24th NHL shutout and improved to 7-1-1 against Colorado.
The Avalanche have lost eight straight on the road, dating to Feb. 14.
The Coyotes needed only 96 seconds to take the lead against Semyon Varlamov. Boedker took a pass from Hanzal, carried the puck into the Avalanche zone and flipped a wrister from the top of the right circle that sailed over Varlamov's blocker for a 1-0 lead.
Hanzal made it 2-0 against the Avalanche's NHL-worst, road power-play unit. He took a pass from Shane Doan on a 2-on-0 breakaway and scored into the vacated left side of the net.
Colorado entered the game having allowed 22 power-play goals in 69 chances over 19 road games, a 68.1 success rate. The Coyotes went 1-for-4 with the man advantage.
Varlamov allowed another tough goal at 7:04 when Gordon bounced a shot from just behind the back line off the goalie's back and into the net for his third goal in six games.
Doan added a goal at 14:37 of the second period when Varlamov overcommitted to a pass from Ekman-Larsson to Radim Vrbata to the top right edge of the crease. Vrbata shipped the puck to an uncovered Doan on the inside edge of the left circle for a shot into the open left side of the net.
Varlamov, who faced only three shots in the third period, finished with 24 saves.
NOTES: Varlamov was playing for the first time in three games. In his prior start, April 1 at Detroit, he allowed three goals on 13 shots. . Gordon didn't score in Phoenix's first 32 games. . Colorado has scored two or fewer goals in six straight games. . The Coyotes are 4-1 when Boedker scores. . Avalanche RW Chuck Kobasew missed his fourth straight game because of a back injury. . Phoenix has scored three second-period goals in consecutive games. . With Smith back in the lineup, Jason LaBarbera was scratched. LaBarbera started five straight games in Smith's absence until he was sidelined by a stomach virus on Thursday.