Brunick made the first throw after being fouled, then intentionally missed the second free throw, leaving the Huskies less than a second to rebound and get to the other end of the court before the final buzzer.
Jordan Boots scored 16 points, including four 3-pointers. Jeff Donnelly contributed nine points, six rebounds and three assists. Andrew Pier made eight points, three steals and four assists.
The Tanagers jumped in front 7-6 at the end of the first period, the score was 20-20 at halftime, and the Tanagers led 33-31 after the third quarter.
Both teams were sharp from 3-point range, with the Tanagers six of nine and the Huskies four of six.
"What a win for these kids," said Coach Jason Huska. "We hung in there and did what we had to do to win. Kyle Brunick stepping up and hitting that free throw was awesome. These kids have believed all year that they can win. I'm happy for them.
"The game was close throughout, and tied with one minute on the clock, and we played keep away before taking the shot which Brunick rebounded," he said.
Vermillion improved its season mark to 11-9, while EP-J fell to 12-8.
Vermillion hit six of 10 from the line. The Tanagers made 16 of 35 field goal attempts, while EP-J was 16 of 34 from the field. The Huskies connected on seven of nine from the line.
Individual stats, Vermillion: Scoring � Jordan Boots, 16, Jeff Donnelly, 9, Andrew Pier, 8, Chonka Wilch, 8, Kyle Brunick, 3. Rebounds � Donnelly, 6, Brunick, 4. Assists � Pier, 4, Donnelly, 3. Steals � Pier, 3.
Individual Stats, EP-J: Scoring � Michael Nebelsick, 13, Sam McInerny, 11, Curt Truhe, 7, Daschle Larsen, 6, Nick Erickson, 4, Eric Brenner, 2. Rebounds � McInerny, 6, Erickson, 4. Assists � Nebelsick, 3. Steals � Nebelsick, 2.
Team rebounds: Vermillion � 19, EP-J � 18. Team fouls: Vermillion � 13, EP-J � 12.