Turco stopped several power-play shots from the Avalanche, the last one by Marek Svatos, before swatting the puck to Sydor as he streaked to centre ice. Sydor took the puck in stride and beat Jose Theodore over his right shoulder.
Sydor began the overtime in the penalty box for slashing after the third period ended.
The Stars' 7-0-3 mark since 1995 is the fourth-longest unbeaten opening-night streak in NHL history. Colorado still owns the NHL's best opening-night record at 15-6-6.
Colorado opened a 2-0 lead in the first period with goals from Joe Sakic and Wojtek Wolski 46 seconds apart. The Stars tied it in the third on goals 28 seconds apart by Mike Modano and Loui Eriksson, then overcame the Avs' power play to beat the team that knocked them out of the playoffs five months ago.
Dallas won a franchise-best 53 games last season only to be eliminated by the underdog Avalanche in the first round of the playoffs.
The Stars added six-time all-star centre Eric Lindros, centre Jeff Halpern, right winger Matthew Barnaby and Sydor, a defenceman, over the summer. Lindros was limited to 33 games last season in Toronto because of a wrist injury.
The Avs' off-season was marked by another exodus of veterans.
Rob Blake, Dan Hinote and Alex Tanguay followed last year's departing class of Peter Forsberg, Adam Foote and Paul Kariya out of town, and Steve Konowalchuk joined them when an EKG revealed a genetic disease that can cause irregular heart rhythms and forced his into retirement.
The Avs are counting on rookie forward Wolski to fill the void left by the Tanguay trade, and he made an immediate impression by scoring one of the Avs' two power-play goals in the first period, when the Avalanche outshot the Stars 22-7.
Sakic scored on a pass from Milan Hejduk across the crease during a 5-on-3 power play at 11:54. Forty-six seconds later, Wolski sent a wrist shot over Turco's left shoulder for a 2-0 lead.
Modano, who relinquished his captainship to Brenden Morrow this season, scored past Theodore from the left circle off a pass from Lindros at 1:28 of the third period, and Eriksson tied it at 2 when he took Stu Barnes' pass from behind the net at 1:56 and flipped it past Theodore.
Notes: The Avs lost their first home opener (5-1-1) since moving to the Pepsi Center. ... Sakic is the league's active leading scorer with 1,490 career points and assists leader with 915.