Smith had 44 saves in his second straight shutout and Whitney passed 1,000 career points with a goal and assist.
Oliver Ekman-Larsson, Antoine Vermette and Radim Vrbata also scored for the Coyotes, who with three games to play are tied with Pacific Division-leading Los Angeles in points with 91 but the Kings own the tiebreaker.
Three of Phoenix's goals came on power plays, all in the second period, for a team that ranks last in the NHL in that category.
Whitney's assist on Vrbata's goal made him the 79th player in NHL history to reach 1,000 points. Forty seconds later, Whitney scored his 24th goal of the season.
"It hasn't been overly easy," Whitney said of reaching the milestone. "I've had to earn what I've done. You know I've been on seven teams. I've been bought out twice. I've been on waivers a couple of times. There's been a couple of times in my career where it didn't look like it was going to go on any further.
"So this is something I'm very proud of."
Jeff Deslauriers, in his third start of the season for Anaheim, had 29 saves.
The Coyotes killed six penalties.
Smith, honored as the team's MVP before the game, earned his seventh shutout of the season, fourth-best in the NHL.
"It was one of those nights where we weren't going to beat that guy," Anaheim coach Bruce Boudreau said. "When Bobby Ryan beats him and hits [Phoenix's] Boyd Gordon in the back of the head and it bounces over the net, nothing was going to go in."
The goalie, who in 3½ seasons in Tampa Bay never got the opportunity he wanted, had two of his best games of the season when the Coyotes needed him most.
"It speaks very well for his maturity in the game," Phoenix coach Dave Tippett said. "He's a player who wants to be in those critical situations."
Smith, who had 15 first-period saves -- 38 overall -- in Phoenix's 2-0 win over San Jose two nights earlier, was even better against the Ducks, stopping 21 shots as Anaheim outshot the Coyotes 21-7 in the opening period.
But Phoenix led, thanks to Ekman-Larsson's timely exit from the penalty box. The Coyotes had just killed the penalty when, after a faceoff at the Phoenix end, Mikkel Boedker got the puck and passed it to Ekman-Larsson. The 20-year-old defenseman broke free and tapped a backhander past Deslauriers, giving the Coyotes a 1-0 lead with 13:50 left in the period.
"It's a team that's not in the playoffs," Smith said about Anaheim, "and they have some firepower up front so we didn't come out of the first period like we wanted to. We were up 1-0, we knew we had to play better, so we came out in the second and third and played to our potential."
The goal came seven seconds after the first of Phoenix's two first-period penalty kills. The Coyotes killed another penalty in the second period, then scored on a power play to go up 2-0.
With Anaheim's Saku Koivu in the penalty box for tripping, Vermette deflected Derek Morris' slap shot into the net with 8:57 left in the period.
The Coyotes made it a rout after the Ducks' Corey Perry locked up with Gilbert Brule in a fight. Perry got an extra two minutes for instigating the fisticuffs. Anaheim had 21 seconds left in a penalty for having too many men on the ice, giving Phoenix a two-man advantage. Sixteen seconds later, Vrbata scored his team-high 33rd goal on an assist from Whitney to make it 3-0.
Whitney, a 39-year-old left wing in his 19th NHL season, drew a standing ovation from the crowd. When play resumed, with Phoenix's advantage down to one man, Whitney quickly scored and it was 4-0 with 3:06 left in the second period.
Phoenix has three games to play, beginning with their final regular-season home game Tuesday night against Columbus. They finish the season at St. Louis and Minnesota.
- Whitney has 47 points in 45 career games against Anaheim.
- The Ducks had beaten Phoenix three times in a row entering Saturday night's game.
- Deslauriers was recalled from Syracuse of the AHL on Feb. 14. He won his two earlier starts for the Ducks this season.
- Phoenix, statistically the worst power-play team in the league, has scored on four in the past two games.