GLENDALE, Ariz. -- Tuesday was a day to remember for both Phoenix Coyotes goalies.
Hours after starter Mike Smith was named to the Canadian team that will compete at the 2014 Sochi Olympics, backup Thomas Greiss recorded the first shutout for a Phoenix goalie this season in a 6-0 win against the Calgary Flames at Jobing.com Arena.
Lauri Korpikoski had a goal and two assists for Phoenix. Mikkel Boedker, Shane Doan, Martin Hanzal and Michael Stone each had a goal and an assist; the Coyotes had seven players with multipoint games.
The Coyotes hadn't won in regulation since defeating the New York Islanders 6-3 here on Dec. 12. Phoenix was 2-4-4 since, with its wins coming during a run of six straight overtime games.
Phoenix coach Dave Tippett decided Monday that Smith would sit against Calgary regardless of how the Olympic selection went. With Smith watching, Greiss completed his second career shutout with 27 saves. He is 6-2-1 this season, lowered his goals-against average to 1.89, and has three of the Coyotes' past five victories.
"It was a must-win for us. We needed those points," said Greiss, whose other shutout came last Jan. 26 for the San Jose Sharks against the Colorado Avalanche. "The guys blocked a lot of shots  that took chances away that made it easier for me. Then we got up a couple of goals and that helps too."
Griess made his best save in the first period, making an acrobatic glove save on a Dennis Wideman power-play shot. But most of the night he made it look easy.
"He just looks solid in there. He doesn't do anything flashy," Tippett said. "When a goaltender makes things look easy, like routine saves, then he's playing well. A couple of the shots he saw were tougher than they looked, but he made the saves and moved it along."
The Phoenix offense took it from there. Doan and Boedker scored their 13th and Hanzal his 12th during the second period, when Phoenix took control with three goals during a span of 10:37. Boedker has career highs for goals and points (29) and three goals and five points in his past four games. He has 14 points in his past 17 games, feeling more comfortable since moving to the right side.
Korpikoski, who will play for Finland in Sochi, has four points in the past two games. It was his first three-point-night since Nov. 16 against the Tampa Bay Lightning, when he had a goal and two assists before suffering an upper-body injury that cost him 13 games before easing back into the lineup.
"It took some time to get my conditioning back and to get used to things like back-to-back games," he said. "But it's coming back and I feel pretty good. I'm happy to be playing in the Olympics, but I want to focus the next month on getting the Coyotes in good position and contributing."
Rob Klinkhammer scored for Phoenix, and Mike Ribeiro and Radim Vrbata each had two assists.
The Flames were shut out for the fourth time in the past six games and have been outscored 16-1 in five losses during that span. They snapped a four-game losing streak with a 4-3 win against the Colorado Avalanche on Monday.
"The first period was a good period. Then we had a couple of bounces and we started to get away from it and get discouraged," forward Mike Cammalleri said. "But we played a team that's had the success they've had by staying patient and sticking with it. We saw the snowball effect. They did it the right way and we did it the wrong way tonight."
Goalie Reto Berra made 24 saves, but was the victim of some bad bounces in the second period.
Boedker ran down a wayward Ribeiro shot behind the Calgary net, and his centering flip deflected first off Berra, then the shoulder of Doan before falling in the net at 2:07. The goal was Doan's first since being sidelined with Rocky Mountain Fever on Dec. 4. The Halkirk, Alberta native has 45 points in 62 career games against the Flames.
Fortune struck again 1:34 later. After two Calgary players were tangled in the Phoenix zone and behind the play, Korpikoski let a shot go that caromed off the back of Vrbata and squirted into the slot, where Hanzal had a gaping net in front of him. Hanzal slid it home at 3:45.
"They get the two breaks and then Phoenix just sat back and waited," Calgary coach Bob Harley said. "If you look at offense, they have more weapons that we do. Their top three lines can all score.
"Last night we were happy with the win, tonight we are not happy. There is no sugar-coating; unfortunately that is part of our process."
The Coyotes took their first three-goal lead in nearly a month (Dec. 12) in a more conventional fashion. Ribeiro dug out a puck behind the goal line and fed Boedker for a one-timer that beat Berra cleanly at 12:40.
Korpikoski punched home his rebound at 9:02 of the third period before setting up Stone for his eighth of the season at 15:36. Klinkhammer made it 6-0 on the power play at 18:38.