Minnesota trailed 2-0 after two periods, but rallied to tie the game in the third period on goals from Nate Schmidt and Zach Budish.
Yale's Kenny Agostino opened the scoring, with a goal midway in the second period to make it 1-0.
The Bulldogs added another goal with four minutes left in the second to make it 2-0, as Gus Young scored on a power play.
Minnesota, ranked No. 1 or No. 2 most of the season in the national polls, was the No. 2 overall seed in the tourney, and the No. 1 seed in the West region.
Yale was ranked No. 15 in two national polls before the tournament.
In the Midwest region, Minnesota-State Mankato (24-13-3) takes on Miami (Ohio) (24-11-5) Saturday. Saturday's other semi-final in the Midwest pits and St. Cloud State (23-15-1) against Notre Dame (25-12-3).
ESPN will air the games online. Here's a complete schedule, via the Star Tribune.
Here's a link to today's game, via ESPN3.