The Capitals (1-1-0) dug out of a three-goal first-period hole for a 5-4 shootout victory over Calgary. The Stars, meanwhile, gave up three in the third to spoil their season opener in a 4-2 home loss to Florida.
Both will try to avoid such 20-minute breakdowns Saturday night in Dallas.
Through two games, Washington fans have been exposed to some quality theater.
The Capitals came back from three one-goal deficits in Tuesday's opener at Chicago and took their first lead early in the third period only to lose 6-4. They trailed 3-0 after one period Thursday and 4-1 midway through the second before rallying to win.
"I think we were really flat coming out, I really do," coach Adam Oates said. "We didn't expect it, but I really thought we were."
Ovechkin and Grabovski each have three goals and two assists through two games. It took Ovechkin 10 games to reach five points last season, and Grabovski finished with 16 points in 48 games for Toronto.
Rookie defenseman Connor Carrick scored in his home debut with his ice time increasing in the final 40 minutes after Jack Hillen left the game with a lower-body injury. Oates said Hillen "is going to be out for a bit."
The poor start Thursday resulted in a goaltending change from Braden Holtby to Michal Neuvirth, but Oates said Holtby would still be his starter in Dallas.
"Everybody has hiccups," Oates said. "Everybody."
Holtby has allowed eight goals through 76 minutes in net, posting an .822 save percentage.
The Stars' bid to kick off 2013-14 on a positive note as they try to end a five-year playoff absence was going well until the last 10 minutes.
Brenden Dillon scored to give Dallas a 2-1 lead 7:32 into the third, but the Panthers scored three unanswered goals from the 10:32 mark.
"We can't take anything for granted," Dillon said. "No lead is safe."
First-year Stars coach Lindy Ruff saw his team get outshot 39-27, including 15-8 in the third.
"We didn't win enough battles," said Ruff, who spent 15 seasons with Buffalo before joining Dallas as part of a makeover by first-year general manager Jim Nill.
Alex Chiasson also scored for the Stars, who had earned at least a point in their last 14 home openers. Kari Lehtonen had won his previous three season openers before losing Thursday despite making 35 saves.
Along with All-Star Jamie Benn, the centerpiece of the Stars' scoring this season figures to be Tyler Seguin, who is familiar with Washington after being traded from Boston in the offseason. He has just three points in 11 career games against the Capitals.
Washington and Dallas haven't played since Nov. 8, 2011, a 5-2 Dallas win. Lehtonen made 30 saves and Benn had a goal and two assists.
The Stars are 8-1-1 in this series dating back to 2002 and 9-0-2 at home against the Capitals since a regulation loss Oct. 17, 1995.