Ville Husso made 38 saves for the Red Wings (13-11-7), who have lost six straight (0-4-2).
"Probably any other time in the season this is a pretty good point on the road," Detroit coach Derek Lalonde said. "The fact that we're on a [rough] stretch leaves you a little bit frustrated, even in overtime. We get the Grade-A, inner-slot chance (by Filip Hronek), we put a dent in the crossbar. Theirs goes post-in from outside the scoring area."
David Perron gave the Red Wings a 1-0 lead at 7:30 of the first period when he received a pass from Michael Rasmussen and lifted a backhand over Lindgren's right shoulder. It was Perron's 10th goal of the season.
Oskar Sundqvist scored a power-play goal at 15:36. Joe Veleno passed to Jonatan Berggren behind the goal line, and Berggren sent it in front to Sundqvist to make it 2-0.
"We played much more of our identity [tonight], hard to play against," Detroit captain Dylan Larkin said. "We forechecked hard, we battled. It was like a playoff game tonight."
Dowd, who missed a 5-2 win against the Toronto Maple Leafs on Saturday due to a lower-body injury, cut it to 2-1 at 15:35 of the second period when he took a pass from Ovechkin and scored on a wrist shot from the high slot, then tied it 2-2 at 15:46 after the ensuing face-off when he redirected Nick Jensen's feed.
"Just some really good stuff by a lot of guys and to see 'Dowder' score a couple, it was great to see," Lindgren said. "He's a guy that works extremely hard. He's a great guy in the room. Thought he played excellent tonight after not playing last game."