Hintz made it 1-0 at 14:08 of the first period when John Klingberg's point shot deflected off his shin pads.
It was Hintz's first game back after he missed seven with a lower-body injury; Klingberg also returned Saturday after missing six games with a lower-body injury.
Maatta scored on a 2-on-1 off a pass from Alex DeBrincat to tie it 1-1 at 17:24.
"I think [Khudobin] cheated over towards me a little bit," DeBrincat said. "[Maatta] was wide open over there. If [Khudobin] was standing in the middle maybe, it's a little different play. But I felt he was inching towards [me], so I gave it over there and luckily it went in the net. He made a good play and good shot."
Khudobin made a sequence of four saves at 2:27 of the third period to keep the game tied. Upon video review by the Situation Room to see if the puck crossed the goal line, the call on the ice stood.
"To be honest, I was 90 percent sure that it wasn't a goal," Khudobin said. "I know [Blackhawks forward Andrew] Shaw was celebrating big-time, but I wasn't hesitating on that one."
Chicago forward Dylan Strome deflected a Maatta shot into the net at 17:00, but the goal was waved off because of a high stick, a call that was also upheld upon video review.
"On the second one, I was 50-50," Khudobin said about the goal possibly counting. "The referee called it right away, but there was replays. I thought it was a little high, but you never know."
Khudobin stopped Blackhawks forward Patrick Kane on a breakaway at 2:20 of overtime.
"There were some pretty big saves both ways, no question," Blackhawks coach Jeremy Colliton said. "We had a couple that maybe could've went in, but that's going to happen. Sometimes you are going to get the bounces and the calls, and some nights you aren't. I thought we did enough to score, and I thought we defended pretty well and got some saves."
Khudobin also stopped both Blackhawks shooters, Jonathan Toews and Kane, in the shootout.
"To be honest, I was hesitating," Khudobin said. "On the first one, I'm lucky that I got the poke check. On the second one, it hit my glove. I didn't know what to expect. I was thinking maybe five-hole or whatever. [Kane's] got quick hands, by the way. But it hit my glove, hit the post, and went out."
Chicago was 0-for-4 on the power play and is 1-for-17 in its past six games. Dallas was also 0-for-4, including a power play at 2:27 of overtime.
