Lindholm scored his second goal of the game from above the left circle on a power play to tie it 5-5 at 13:10 of the third period.
Earlier in the period, the Coyotes scored twice in 1:06 to take a 5-4 lead, on goals by Andrew Ladd at 8:35 and Phil Kessel at 9:46.
"We got away from our game a little bit there, definitely gave them a little too many [Grade A] scoring chances," Lindholm said. "We kind of got back to our game, but then we had a breakdown and they scored, and then we kind of went back to bad habits again. It was a roller coaster of a game."
Boyd gave Arizona a 1-0 lead at 2:46 of the first period.
Lindholm, Kevin Shattenkirk and Derek Grant scored in a 2:54 span to give Anaheim a 3-1 lead. Shattenkirk scored his first power-play goal since March 6 to tie it 1-1 at 5:47; Lindholm finished a 3-on-2 for a 2-1 lead at 6:44; and Grant redirected Jakob Silfverberg's shot to make it 3-1 at 8:41.
"The first 10 minutes of that game, it was not pretty," Arizona coach Andre Tourigny said. "Anaheim was hard on us and we didn't react well."
Coyotes forward Christian Fischer scored on the power play to make it 3-2 at 15:12. It was his first goal since Oct. 31 against the Carolina Hurricanes.
The Ducks went 13:36 without a shot on goal in the second period before Max Comtois' breakaway at 19:12. Keller then went the other way shortly after and scored on a breakaway to tie it 3-3 with 34 seconds left in the second period.
"That's a swing in the game," Tourigny said. "It could have hurt us a lot with that goal [if Comtois scored]. Another big save for [Wedgewood], and right away after we got our own breakaway, and [Keller] scored a big goal there. That was a huge swing in the game, no doubt about it."