Vladislav Namestnikov scored and Thomas Greiss made 20 saves for Detroit (2-4-1), which is 0-2-1 on a four-game road trip.
"If we can play like that on a consistent basis we're going to give ourselves a chance to win most games," Red Wings coach Jeff Blashill said. "If you play like we did (Sunday) against [the] Chicago [Blackhawks, a 6-2 loss], you don't even give yourself a chance."
Namestnikov gave Detroit a 1-0 lead at 11:37 of the first period with a backhand between Khudobin's legs. It was his first goal after signing a two-year contract as a free agent Oct. 11.
"I had plenty of opportunities to score, but that's how hockey goes," Namestnikov said. "I'm glad to get my first one for the Red Wings, but it would have been nice to get the win."
Klingberg tied it 1-1 with a power-play goal at 5:27 of the second period, scoring on a point shot through traffic with an assist from Pavelski. It was Dallas' ninth power-play goal in its first three games, one short of the NHL record set by the 1975-76 Montreal Canadiens.
"If you go back to the playoffs in Edmonton, [Klingberg] was our best defenseman, and that hasn't changed," Bowness said. "He wants to be out there in every key situation, and he wants the puck. That's when he's at his best."
Klingberg has scored six points (one goal, five assists) in three games.
"I don't think my job is to sit back and wait for the game to come to me," Klingberg said. "I wasn't overly happy with our game tonight. We got the two points, but we have a higher standard and we need the intensity to ramp up when we play them again [Thursday]."
Stars forward Roope Hintz was a late scratch with a lower-body injury. Mark Pysyk switched from defenseman to forward.
"We didn't know what our lineup was going to be until we got to the building," Bowness said. "We signed Mark to play defense, but luckily he played some right wing for [the] Florida [Panthers] last season and he was able to step up and do a nice job."
NOTES:Dallas has won five straight against Detroit at home. … Pavelski has scored 372 goals with 428 assists in 15 NHL seasons. He is the ninth player to score 800 points after being selected in the seventh round or later in the NHL Draft. … Dallas is 9-for-16 (56.3 percent) on the power play, which leads the NHL. … Red Wings forward Dylan Larkin, who entered the game averaging 22:00 of ice time, played 17:04. Blashill said Larkin was unavailable for part of the game but did not elaborate. … It is the third time in NHL history that the previous Stanley Cup finalists each began with three straight wins. (1975-76, Philadelphia Flyers 4-0-0, Buffalo Sabres 8-0-0; 1965-66, Montreal Canadiens 3-0-0, Blackhawks 4-0-0). The Tampa Bay Lightning, who won the Cup last season, were 3-0-0 before losing Saturday.
