Jeff Halpern scored on a rebound with 2:28 left for the Stars, who fended off three power plays with some nice saves by Mike Smith in the final 12 minutes to win their third straight game.
All-star goalie Marty Turco was pulled from his second straight start for the Stars, yanked after giving up two goals in less than a minute midway through the second period. Colorado's Peter Budaj had been replaced earlier in the period after Dallas went ahead 4-1.
Within a minute after rookie Wojtek Wolski scored to get Colorado within 4-3 and chase Turco, the Stars stretched the lead. Halpern knocked the puck to the front of the net and Joel Lundqvist deflected it over the shoulder of Jose Theodore.
Boucher's goal later in the second period made it 6-3.
Smith, who started and had a shutout Saturday against Anaheim, gave up two goals in the first five mintues of the second period. But he stopped point-blank shots by Wolski and Joe Sakic during power plays, then made a sprawling save to deny Ian Laperriere with 3:13 left.
The Stars have won five of their last six games. With 70 points, they're only four points behind Pacific Division-leading Anaheim and one point behind second-place San Jose.