The three-goal outburst erased an early 1-0 deficit and Giguere stopped 12 of the 13 shots he faced in the third period.
The Ducks play five of their next seven games at home, where they are 13-7-5-1 this season.
Jason Krog picked up assists on all three goals - his first career three-point game.
Mike Johnson had a power-play goal and Paul Ranheim scored midway through the third for Phoenix, which has lost three of four following a three-game winning streak.
"It was a tight game today, we had a little letdown in the second period," Coyotes defenseman Teppo Numminen said. "We kind of got off our system and they got a couple of 3-on-2s and 2-on-1s there and that was the game."
After a scoreless first period in which the teams combined for 18 shots, Johnson staked the Coyotes to a 1-0 lead 2:17 into the second. Rookie Ramzi Abid stuffed a rebound off Johnson and past Giguere.
Kjellberg knotted the contest just under six minutes into the period, scoring his sixth goal of the season. It was his first goal since December 29 - a span of 17 games.
Chistov made it 2-1 with 10:06 left in the period, beating Phoenix goaltender Zac Bierk to the glove side with a wrist shot from between the circles.
Havelid made it 3-1, one-timing a pass from Samuel Pahlsson past Bierk. It was Havelid's career-high ninth goal and 26th point. He had just 26 points in his first three seasons in the league.
Ranheim's first goal of the season, midway through the third period, got the Coyotes within a goal.