Richards had the lone goal of the shootout and Raycroft made 22 saves before stopping all three shootout tries he faced as the Stars beat Carolina 2-1 on Friday night, keeping the Hurricanes winless in Dallas since moving from Hartford in 1997.
Richards beat Cam Ward over the pad, and backup goaltender Raycroft stopped Eric Staal's wrist shot in the third round to secure the extra point and give the Stars a 9-0-1 mark in their last 10 games.
"I went in with speed, slowed down a little bit to see if I could get (Ward) backed up," said Richards, 3 for 5 in shootouts this season. "I wanted to shoot and he didn't give me that, he's a good patient goalie, so I had to think of something quick and I'm lucky I got it up at the end."
The Hurricanes haven't won in Dallas since Feb. 11, 1996, when they were still the Hartford Whalers. Dallas is 9-0-1 in the 10 meetings since the move.
The Stars got a boost from Raycroft, who stepped in again as starter Kari Lehtonen sat out with back spasms. Raycroft is expected is expected to start Saturday night at Phoenix.
"Andrew Raycroft was just outstanding," Stars coach Marc Crawford said. "What can you say about Brad Richards? He just finds a way to score and it's such an important element in today's NHL, that you've got the shootout. Tonight, we only needed the one goal, so that's great when you've got your goaltender playing as well as Andrew Raycroft played for us. It's a huge two points."
Ward made 28 saves and Jiri Tlusty scored for the Hurricanes in regulation.
Both teams had chances to win in overtime. Brenden Morrow nearly won it for Dallas 90 seconds into the extra period, but his rebound shot glanced off the post. Ward robbed Richards halfway through the five-minute period, and Raycroft made a big glove save on Joe Corvo with 42.4 seconds remaining.
The Hurricanes got little consolation from getting one point. Carolina is 3-5-4 in its last 12 games and 1-4 in shootouts.
"It's always tough when you lose in a shootout," Ward said. "I thought it was a pretty up-tempo game, both teams were pretty stingy. And then Raycroft makes that great save (on Corvo) in overtime to put it into the shootout, and then the thing about the shootout is it's a flip of a coin. It can go good or it can go bad."
James Neal scored for Dallas at 9:39 of the first period when he controlled the puck to the left of the net, waited for Ward to make the first move, then lifted a shot into the top left corner.
Tlusty tied it by beating Raycroft from the slot at 9:03 of the second period.
Material from wire services was used in this report