Turgeon and Arnott accounted for both goals in a 2-1 victory over the Toronto Maple Leafs, spoiling Belfour's return to the city where he won a Stanley Cup.
A member of the Stars' Stanley Cup winning team in 1998, Belfour played five seasons in Dallas before signing with Toronto as a free agent.
"It was emotional," said Belfour, who holds the Stars' franchise record for wins (160). "I had a lot of mixed emotions, but I have great memories here. It was exciting to come back."
Belfour had his worst season with the Stars last year and experienced problems off the ice, including an alledged assault of a hotel security guard in Dallas in March 2000 and a publicized argument in January 2001 with then-coach Ken Hitchcock regarding an optional practice.
Despite his troubles, the crowd recognized Beflour as the player who brought them a championship and cheered him as he was announced as the starting goaltender.
"I heard the crowd and it's a great feeling," Belfour said. "The fans have always been good to me."
The Stars wasted little time in getting to their former teammate. Just 2:13 into the contest, defenseman Phillipe Boucher's shot deflected off teammate Jere Lehtinen and to Turgeon, who fired the puck into an empty net.
Arnott extended the lead to 2-0 at 3:52 of the second period when he took a back pass from Bill Guerin and wristed it past Belfour.
"We talked about having a good start and we're doing that at home," Dallas coach Dave Tippett said. "But they can't all be Picassos."
The Stars improved to 5-0-0-1 at home, and have allowed just eight goals in the six games.
Belfour, who has struggled since recording a shutout in the season opener, finished with 21 saves.
"I was seeing the puck really well tonight," Belfour added. It definitely would have been nice to get the win, but we just fell short."
Marty Turco, who was kept by the Stars because he was younger and more inexpensive than Belfour, turned aside 22 shots. He has allowed just four goals in his last three starts.
"It's always nice to win," said Turco, who backed up Belfour the last two seasons. "It was special for everybody. With the buildup for the game, the guys really came out flying."
Turco survived 10 shots in the third period including several flurries with time winding down.
"We wanted to make sure pucks got out of there," said Bill Guerin, who assisted on Arnott's goal. "Marty came up big at the end and made some big saves for us."
Tom Fitzgerald scored Toronto's only goal, beating Belfour with a slap shot inside the blue line with 7:48 remaining.