Klemm had a goal and an assist for his first two points of the season, Marty Turco stopped 20 shots and the Stars beat the Edmonton Oilers 3-2 on Saturday night.
Klemm, moved from defence to right wing by coach Dave Tippett earlier this week, was scoreless in his first 11 games this season.
"I'm not out there for my speed," Klemm said with a laugh. "I've played the wing earlier in my career, in '96 for Colorado, so it's not something new for me."
Jere Lehtinen and Philippe Boucher also scored and Eric Lindros had two assists for the Stars, winners of three of their last four.
Dallas' depth on defence made Klemm a healthy scratch in 24 of the Stars' first 35 games this season.
"It's nice to be involved instead of sitting in the stands and watching," Klemm said. "It's especially good to contribute offensively to a win."
Tippett is using Klemm on a line with Lindros and Matthew Barnaby, and the trio was effective against the Oilers.
"That's what you call efficiency to the max," Tippett said. "That line had a real purpose to the game. You want the other team to know you're in the game and they did that tonight."
Barnaby said Klemm's addition to the line is valuable because Klemm is very familiar with defensive positioning.
"(Klemm) is a hard worker who knows his role on defence," said Barnaby, whose assist on Klemm's goal was his 300th point. "He gets the puck deep and keeps the game simple."
In the teams' last meeting on Dec. 8, the Oilers came away with a rare win in Texas, 2-0. With the latest loss, the Oilers dropped to 4-20-2 in regular-season games in Dallas since the Stars moved from Minnesota in 1993.
Marc-Andre Bergeron and Joffrey Lupul scored power-play goals for the Oilers, who've lost five of their last seven. Dwayne Roloson had 23 saves for Edmonton.
Oilers coach Craig MacTavish said his team remained competitive even after falling behind by three goals.
"In the second period, we started coming on and they got a few breaks around the net," MacTavish said. "I never felt like we were going to be out of the game. When it was 3-0, I thought the game was getting away from us but I was still pretty confident we could get back in it."
Aggressive forechecking by Lindros led to Klemm's first-period goal. Lindros forced Edmonton defenceman Ladislav Smid into a turnover behind the Oilers' net and Lindros passed to Klemm, who skated up the right wing and notched his first goal of the season at 10:44 of the opening period.
"My linemates did a great job getting me the puck," Klemm said.
Lehtinen made it 2-0 at 6:02 of the second period, converting Jussi Jokinen's centering pass.
Boucher extended Dallas' advantage to 3-0 less than two minutes later when he scored his 12th of the season from beyond the right circle.
Bergeron's goal while the Oilers skated 5-on-3 in the second period cut the deficit to 3-1. Edmonton broke a drought of six games and 30 opportunities with the man advantage. Bergeron registered the Oilers' last power-play tally on Dec. 8 against the Stars.
Lupul made it 3-2 when he lifted a power-play rebound over a fallen Turco with 30 seconds left in the second period.
"We showed signs of life on our power play in our last game in Phoenix," MacTavish said. "Normally that's a sign that things are turning around."
The Stars remained without centre and offensive catalyst Mike Modano (hip flexor/groin injury), who missed his ninth straight game. Dallas is 5-4 since Modano's injury.
Notes: Klemm scored his first goal since March 22, 2006. . . . Boucher has points in 10 of his last 12 games and is tied for the NHL lead in goals by defencemen. . . . Still out for the Oilers were Ryan Smyth (fractured right thumb, missing his 10th straight game) and Ethan Moreau (dislocated right shoulder, sitting out his 27th in a row).