Ryan McLeod scored, and Stuart Skinner made 29 saves for the Oilers (13-5-0).
"When we give up two power-play goals -- actually three, one right at the end of it -- you're chasing the game," Tippett said. "Against a heavy team like that, they're going to play in front of the puck all night and you get behind, it's hard to jump back in."
Dallas took a 1-0 lead on the power play when Klingberg's point shot was deflected by Alexander Radulov and went off the stick of Hintz at 10:59 of the first period.
"They moved around well," Oilers defenseman Cody Ceci said about the Stars power play. "They've [got] two pretty balanced power plays and they showed it tonight. We'll have to take a look at it, but we'll have to move on pretty quickly because we have another game tomorrow night (at the Arizona Coyotes)."
Jason Robertson made it 2-0 on the power play at 15:59 when he finished off a tic-tac-toe passing sequence from Klingberg and Hintz from the right face-off circle.
"I think [the power play] has been good the entire year," Klingberg said. "You're not going to score every time, but you can build momentum out of it. We've got two really good units battling for the ice time, so it's what you need. I think when you're competitive like that, you want to be on the ice. Both units are really feeling it right now, so it's a good thing."
Denis Gurianov made it 3-0 at 9:27 of the second period after Klingberg sprung him through the neutral zone for a breakaway. The goal came four seconds after a Dallas power play expired.
"We played great team efforts at times," Stars forward Joe Pavelski said. "A lot of little things, blocked shots, things that throughout a game a team feeds off of. We've simplified a couple things, but good commitment, minds are settling in a little bit, guys are feeling the puck a little bit. It's going in the net at times. Understanding our game, we have to be patient at times, and knowing that we're going to create our chances."