The 39-year-old Modano, who has 555 career goals, picked up a loose puck and beat Colorado goalie Craig Anderson on a wrist shot with 12:59 left to help give the Stars their fifth consecutive victory at home.
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.
Alex Auld made 24 saves and won for the fourth time in his last five starts for the Stars, who had lost the previous two meetings this season to the Avalanche by a combined 8-1 score.
Modano has 1,351 points, moving past Mats Sundin into sole possession of 25th place in the career list. It was Modano's first two-goal game since Dec. 3, 2008, against Edmonton.
The Stars won their second straight for the fifth time. They haven't won three in a row this season.
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, who has six goals in eight games, 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.
NOTES: 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.