Patrick Maroon’s power-play goal put Chicago back ahead 2-1 at 10:24 after he received a pass to the side of the net, turned and scored far side.
Teravainen extended it to 3-1 at 13:16 when he scored with a wrist shot from above the hash marks.
Jackson LaCombe cut it to 3-2 at 14:41 after scoring off his own rebound.
Reichel made it 4-2 at 4:53 of the third period on the breakaway 11 seconds after the Blackhawks killed an Anaheim power play.
Reichel had been a healthy scratch the previous two games.
"It felt good to be back. It's not always easy if you got scratched," Reichel said. "First game back, timing is a little off, but I tried to make the best of it, stay positive and play a little [mad]. I'm glad it worked out."
Donato scored 36 seconds into a 5-on-3 advantage to push it to 5-2 at 7:40 after Alex Killorn and Gudas each committed minor penalties.
"The fourth goal really got us down to our knees," Gudas said. "It’s very hard to come back, especially this late in the hockey game against anybody."