Stu Barnes and Stephane Robidas also scored, and Mike Modano added two assists to help the Stars halt Colorado's season-best six-game winning streak.
Turco, who stopped 11 shots in a busy second period, improved to 30-16-4 this season, giving him five straight seasons of 30 or more victories.
The Pacific Division-leading Stars have 89 points, maintaining their one-point edge over the runner-up San Jose Sharks. Earlier on Sunday, the Sharks beat the Minnesota Wild 3-2 in a shootout as San Jose took over the division's top spot for a few hours.
Richards had five assists in his first game with the Stars after being acquired from Tampa Bay in a five-player trade on Feb. 26. But Richards had been without a point in his next two games until he collected a goal and an assist Sunday.
Center Peter Forsberg was out for the Avs with a groin injury sustained in Saturday's 3-1 win over Dallas in Denver and is listed as day-to-day.
Forsberg re-signed with Colorado on Feb. 25 and has two assists in three games, both coming in Saturday's win.
The Avs had been 9-3-1 in their last 13 road games, but the Stars jumped out to a 2-0 lead in the first 5:25 against starting goaltender Jose Theodore.
The Stars came out with a much harder edge than they did Saturday, building a 12-1 shots advantage in the first period.
Barnes notched his ninth of the season on a rebound at 3:56 of the first period, and Robidas made it 2-0 at 5:25 with his seventh on a shot from just inside the blue line that got past a screened Theodore.
Richards' one-timer from the right circle at 6:55 of the second period was his 19th goal of the season, stretching Dallas' lead to 3-0.
Avalanche head coach Joel Quenneville lifted Theodore after two periods, replacing him with Peter Budaj.
Notes: Colorado's six-game winning streak was its longest since taking eight in a row from Dec. 31, 2005-Jan. 17, 2006. ... Dallas nearly held an opponent without a shot in a period for the fifth time in franchise history, but Scott Hannon's shot in the final minute of the opening period glanced off Turco's shoulder. The last time a Stars opponent failed to get off a shot in a period was Colorado on Jan. 10, 2004. ... Modano's assist on Robidas' goal was the 750th of his career. ... Turco had his 10th career win over Colorado and first shutout against the Avs. ... The teams ended their season series by splitting the four games.