Stars coach Marc Crawford has made it a priority to give Modano time off in between games so the 39-year-old star will be fresh for the stretch run.
That plan has paid dividends, withd Modano scoring six goals in eight games.
"I've been feeling much better lately," said Modano, who has 12 goals this season and 555 overall. "I've been able to rest up and primarily focus on games."
Modano picked up a loose puck and beat goalie Craig Anderson with a wrist shot with 12:59 left to help give the Stars their fifth consecutive home victory.
It was Modano's first two-goal game since Dec. 3, 2008, against Edmonton. Modano has 1,351 points, moving past Mats Sundin into sole possession of 25th place on the career list.
"He's still a dangerous player," Colorado center Paul Stastny said. "He has an unbelievable release and still has one of the best shots. He's still a threat out there and it showed tonight."
Colorado, which had its six-game winning streak snapped Thursday night, lost its second in a row. Matt Duchene and T.J. Galiardi scored for the Avalanche.
Anderson had allowed one goal or less in each of his past five starts, making 27 saves in shutting out Dallas on Sunday. He stopped 28 shots Friday.
Colorado had beaten the Stars 8-1 in the first two meetings this season.
"They play a hard-nosed game here," Anderson said. "They have their fans behind them and have a lot of energy here. Obviously, they played a lot more physical tonight than a couple of nights ago."
Alex Auld made 24 saves and won for the fourth time in his last five starts for the Stars. He stopped all 11 shots he faced in the third period.
The Stars won their second straight for the fifth time. They haven't won three in a row this season.
Dallas moved within two points of the final playoff spot in the Western Conference. Nashville and Detroit are tied for seventh place with 61 points.
"We want to put a run together and get in a playoff spot," Stars left wing James Neal said. "These points right now are going to mean a lot in the end."
Modano said a key was getting an early lead against a team it had struggled against.
"We get off to bad starts and try to play catch-up with a team that's quick and fast," Modano said. "We've dug ourselves holes we can't get out of."
Dallas scored first when Jamie Benn redirected Steve Ott's shot past Anderson at 3:18 of the first.
The Avalanche tied it 36 seconds later when Duchene, the top rookie scorer in the NHL with 36 points, beat Auld for his 17th goal of the season.
The Stars took a 2-1 lead on an unconventional goal from Modano.
Modano attempted a centering pass from behind the net. Instead, the puck bounced off Colorado defenseman Kyle Cumiskey and into the net at 7:55 of the first.
Galiardi's eighth goal tied it at 2 at 10:56 of the second period.
Modano scored his 91st career winning goal and tied Wayne Gretzky for 13th place on the career list. ... The Avalanche activated defenseman Adam Foote (sprained ankle) and he played for the first time since Jan. 8. ... Ott, who had an assist, has seven points in his last nine games. ... Colorado has allowed just one power play goal the last seven games, killing 27 of 28 chances. The Stars were 0 of 2 with the man advantage.