Dickinson gave the Stars a 1-0 lead at 4:59 of the first period, skating in from the left wall following a turnover and scoring his first of the season on a backhand from in front.
"It always feels nice scoring," Dickinson said. "So it's nice to get it out of the way and stop fighting myself in the head."
Getzlaf tied it 1-1 at 8:17, intercepting a pass in the left circle before beating Bishop glove side. Roman Polak scored to make it 2-1 at 11:30 on a backhand in the crease.
Getzlaf tied it 2-2 at 3:09 of the second period, receiving a pass from Nick Ritchie from behind the net and scoring short side from the left circle.
Heiskanen, who was the No. 3 pick in the 2017 NHL Draft, scored off a cross-ice pass from Jason Spezza on a 2-on-1 to give the Stars a 3-2 lead at 4:53.
Heiskanen (19 years, 99 days) became the second youngest defenseman to score in Starts/Minnesota North Stars history (Ron Meighan, 18 years, 207 days), and the youngest to do so since the team moved to Dallas.
"That first goal, of course, was a great feeling," Heiskanen said.
Mattias Janmark extended the lead to 4-2 at 11:16, taking a stretch pass at the Anaheim blue line from Julius Honka and scoring on a wrist shot in the slot.
Dickinson scored his second of the game to make it 5-2 at 18:06, beating Gibson on a shot from the slot after Tyler Pitlick sent him a pass from behind the net.
Getzlaf called the overall defensive play by Anaheim "embarrassing."
Said Ducks coach Randy Carlyle, "They're coming up with more pucks than we are. Our commitment to getting the puck back or winning that 1-on-1 battle has to go up."
