Stankoven had two goals and two assists, Jamie Benn had a goal and three assists, and Miro Heiskanen had four assists for the Stars (38-17-9), who hadn't played since a 3-2 shootout win against the Sharks on Saturday. Jake Oettinger made 14 saves.
"I think when you play an 82-game schedule, you've got to find all kinds of different ways to win games. 1-0, 2-1, 7-6," Dallas coach Pete DeBoer said. "I think that's probably the only silver lining tonight, we found a way to come out of here with two real important points. Obviously, didn't play the game we wanted to. You don't want to get in a shootout like that. That's not our game, but we found a way and we'll move on."
Anthony Duclair had two goals and two assists, Fabian Zetterlund had a goal and two assists, and Mikael Granlund had a goal and an assist for the Sharks (15-39-7), who have lost eight straight (0-6-2). Kahkonen made 33 saves.
"This one stings, probably worse than the 10-1, 10-2 losses," Duclair said.
Stankoven got the Stars to within 6-4 at 12:58 of the third period. Following a turnover in the neutral zone, he skated into the left circle and scored with a shot that trickled past Kahkonen.
Johnston cut it to 6-5 at 13:41, banking in a shot from the left post. He then tied it 6-6 at 15:42 after he got to the rebound of Heiskanen's point shot, which had caromed off the end boards.
"I really liked what we did after we got up 6-3," San Jose coach David Quinn said. "We were staying above them and playing a good, smart third period. And then one mistake ends up in the back of our net and you could just feel the uh-oh feeling on the bench."