Ryan Miller made 36 saves for the Ducks, who lost for the first time in five games.
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Anaheim (31-21-11), which has scored two goals or fewer in six of its past seven games, is tied with the Calgary Flames for third place in the Pacific Division, one point behind the San Jose Sharks for second.
"I didn't think that we paid enough of a price to be inside and on top of the goaltender," Ducks coach Randy Carlyle said. "We played the turnover game. We were too cute. You can't be cute in the NHL. You've got to get inside and get people and pucks to the net."
Raanta made 40 saves in a 1-0 win against the Edmonton Oilers on Feb. 17, his first shutout with the Coyotes.
"I think when you get the first one, the second one is a little easier to get," said Raanta, who has made the save on 266 of 284 shots (.937 save percentage) in nine games (eight starts) in February. "It took a little time to get the first one, but I think our five-man units are really good right now and they are helping me a lot. We didn't give too many Grade A chances to the other team. If the goalie can be patient and make the first save, the guys are taking care of the rest."