DALLAS (AP) -- By solving their first-period problems, the Tampa Bay Lightning also figured out how to win on the road.

Goals by Vincent Lecavalier and Fredrik Modin gave the Lightning their first lead after 20 minutes this season and Tampa Bay held on for its first road win, beating the slumping Dallas Stars 2-1 Saturday night.

The victory was extra special for Tampa Bay coach Steve Ludzik, who is trying to mold his club after the Stanley Cup champions. It also was the first time the Lightning beat the Stars since Feb. 19, 1996, and it was only their second win in Reunion Arena, the other coming in 1993.

"We've been trying to build a smart, checking team like Dallas," he said. "Tonight shows if we can play like them, we can beat them."

The Stars are going through a bit of an identity crisis as they work a group of faster, younger players into the lineup. They've scored just nine goals while going 2-4-1 over their last seven games.

"We've got to hang tight and work through it together," said center Mike Modano, who had an assist on Brett Hull's first-period goal. "We've got to accept that goals aren't coming right now and find other ways to win."

The sluggish performance was exactly what Dallas didn't want in its final game before Wednesday night's Stanley Cup finals rematch with Buffalo.

While the Stars were playing on four days' rest, the Lightning were coming off losses Wednesday in Buffalo and Thursday in Boston. In those games, and another road loss earlier in New Jersey, Tampa Bay had been outshot 39-13 and outscored 6-1 in the first period.

This time, the Lightning broke out early, outshooting the Stars 13-8 in the opening period and getting both their goals.

Lecavalier got it started 2:54 into the game when he picked off a lazy pass from Dallas forward Mike Keane at the Stars blue line and beat goaltender Ed Belfour one-on-one.

Dallas tied the game when Hull, using a stick with orange grip tape that had a jack-o-lantern drawn on it in honor of Halloween, drilled a slap shot past goaltender Dan Cloutier. It was his fourth goal of the season, all on power plays.

Tampa Bay regained the lead with 14.9 seconds left in the period when Chris Gratton won a faceoff and directed the puck to Modin, who one-timed it past Belfour from just outside the left circle.

Despite being down 2-1, the Stars hardly challenged Cloutier in the second period. They were more aggressive in the third, especially on a power play that produced five shots.

But Cloutier stopped them all.

Dallas, playing with Joe Nieuwendyk and Richard Matvichuk for the first time in two weeks, almost got a fluke goal with 1:14 left when a soft shot by Hull bounced under Cloutier's outstretched leg. The puck hit the post and bounced out, and the Stars couldn't get another shot on goal, not even with six skaters.

"I would've been happy with one point," said Cloutier, who stopped 22 shots. "To get two is incredible."

Belfour had 29 saves, including several tough ones that kept the Stars close.

Dallas fans at least proved they're ready for the Sabres. One of the loudest cheers of the night came when the scoreboard showed that Buffalo lost 3-0 to Boston.

"Right now, we're playing very stale," Keane said. "We're not going to sneak up on any teams."