"Talent is talent," Stars center Brad Richards said. "He's got size and speed. When you see [Modano], he doesn't seem or act like he's 38. He's one of the great players who's ever played."
In his 19th NHL season, Modano is tied for second on the club in goals and fourth in points.
Modano, the career goals leader among U.S.-born players with 540, scored on a one-timer from the top of the right circle off a pass from Brad Richards.
It was Modano's third winning goal this season.
"Time was winding down," Modano said. "I was just trying to get something heavy on the net."
The Stars, who have spent most of the season in last place, improved to 5-1-1 over their last seven.
"We have to keep a playoff mentality and we just need to keep pushing," Ribeiro said. "We've been showing some good worth ethic. So we'll try to keep this run going."
Anaheim's Brendan Morrison scored two goals in the third, including one with 3:19 left that gave the Ducks a 3-2 lead.
"These are tough ones to swallow," Anaheim coach Randy Carlyle said. "You've got to be careful that these kinds of games don't tear the heart out of your team. We weren't rewarded for the work we put in."
Rookie James Neal had a goal and an assist, and Richards also scored to help the Stars win their fourth in a row at home.
Giguere made 34 saves, and Turco stopped 19 shots.
Neal, who had his first career three-goal game Tuesday night at Toronto, scored on a power play 1:06 into the final period to give the Stars a 2-1 lead.
The Ducks tied it midway through the third when Morrison scored his first goal of the night. Morrison, who scored two goals Tuesday night in a loss to Calgary, gave Anaheim the lead late in regulation when he took a centering pass from Bobby Ryan and beat Turco. Morrison has six goals in his last eight games.
Ribeiro, who also had two assists, tied it to set the stage for Modano's 12th goal of the season and his ninth career overtime goal.
"When you can play like he can, you can stay as long as you want," Ribeiro said about Modano "He isn't missing a beat. He's a big key to our team."
The Ducks, who lost a lead in the third to the Flames, have dropped six of seven on the road.
"You get down when you don't work hard and aren't in the game," Carlyle said. "We played closer to the style we need to have success on the road."
Toby Petersen backhanded a pass to Richards, who beat Giguere from the left circle to tie it at 1 at 8:27 of the second. Richards has goals in four straight games and has 10 points over his last five.
Modano, who had two points, has 78 career points against the Ducks -- the most against Anaheim. ... The Ducks need six wins for their 500th franchise victory. ... The Air Force football team was in attendance. The Falcons are preparing to play Houston in the Armed Services Bowl on Wednesday.