Miettinen's fifth goal of the season came only two minutes after Eric Lindros stormed through the slot and took a cross-ice pass from Mike Modano to score the tying goal.
The Avalanche, who eliminated Dallas in the first round of the last two playoffs, jumped out to a 2-0 lead on two goals by Marek Svatos in the game's first seven minutes and chased goalie Marty Turco.
Stars captain Brenden Morrow scored twice in the final three minutes of the first period to tie the game 2-2. But he later left with an unspecified injury.
Morrow appeared gimpy when he came off the ice during a shift change midway through the second period. He didn't return, and the Stars said he had a "lower body injury."
After the teams traded goals in the second period, the Avalanche took a 4-3 lead on John-Michael Liles' one-timer with a two-man advantage in the opening minute of the third period.
Liles took a pass from Joe Sakic and slammed the puck past rookie goalie Mike Smith. Smith came on, after Turco allowed two goals on five shots, and made 18 saves.
Sakic also assisted on the first two Colorado goals. His 929 career assists matched Larry Murphy for 13th on the NHL career list.