Sullivan netted the tying goal with 6:28 remaining in regulation -- his first goal in 14 games -- and then scored the lone goal in the shootout to lift the Coyotes past the Anaheim Ducks 5-4 on Saturday night.
"Scorers like to score and they get frustrated when they don't score," Tippett said. "There are times with a player like that, if he's not getting chances and he's not around it, there'd be some concern. But he's been around it, and if you do that enough you're going to be rewarded."
Lauri Korpikoski scored twice, Matthew Lombardi added a goal, and Mike Smith stopped 31 shots through overtime and then all three shootout attempts for the Coyotes, who won for the second time in three games.
"I just got in the right spots, and I don't think Smith was ready for them," Cogliano said of two of his goals. "I just wanted to shoot at the net quickly, and they went under him."
The teams were playing the first of three consecutive games against each other.
"(Smitty) made some timely saves," Tippett said. "No goalie likes to give up four goals. But if you look at the saves he made, he kept them off the board on their early power play.
"Then, between the power play in overtime and the shootout, he won the game for us."
Cogliano opened the scoring 21 seconds in, taking a pass from Koivu from behind the net and scoring on a one-timer from the top left edge of the crease.
Korpikoski made it 2-1 at 12:32 of the period when Fasth missed the puck with his glove on a shot from the top of the left circle, but Cogliano answered 27 seconds later to tie it again.
"I think they were getting a little tired," Korpikoski said of the Ducks, who played for the second straight night and for the fifth time in seven days. "We just came at them in the third and found a way to get the goals."
Cogliano helped draw a goaltender interference call against Kyle Chipchura with a subtle one-handed push to Chipchura's back just outside the crease.
Koivu took a pass from Bobby Ryan between the circles and beat Smith with 3 seconds left in Chipchura's penalty to give the Ducks a 4-3 lead.
"We're going to feel like we let a point get away, giving up the leads a couple of times," Ryan said. "We looked and felt as tired as we have all season. We were a pretty tired group, you could see it in the legs."
Anaheim was called for one penalty, a coincidental roughing minor on Koivu. ... Cogliano's other hat trick was February 1, 2012, also in Glendale against the Coyotes. ... Ducks C Kyle Palmieri left the game late in the first period because of an upper body injury and didn't return. ... Coyotes captain Shane Doan assisted on Lombardi's goal, giving him 29 goals and 36 assists in a team-leading 89 career games against Anaheim. ... Lombardi's goal was the 99th of his career. ... Phoenix has played three straight against one team one other time, facing San Jose three times in six days. Anaheim, which never has played three consecutive games against the same team, will do it again in April against Dallas in a five-day span. ... Anaheim D Sheldon Souray returned to the lineup after being a healthy scratch in the Ducks' 3-2 win over Minnesota on Friday.