Brunette, a forward from Sudbury, Ontario, played junior hockey for Owen Sound of the Ontario Hockey League, where his teammates included future NHL forwards Kirk Maltby and Scott Walker, and goalies Kevin Weekes and Jamie Storr. He had a breakout season in 1992-93, scoring 62 goals and 162 points, and the Washington Capitals selected the 20-year-old in the seventh round (No. 174) of the 1993 NHL Draft.
He played most of the next three seasons in the minors before earning his first NHL call-up midway through 1995-96. Brunette made his NHL debut against the Chicago Blackhawks on Jan. 17, 1996 and scored his first goal against the Florida Panthers on Feb. 29, 1996.