He primarily pitched middle relief, but he did start four games in his major league career, three of which were in his rookie season.

He worked his way through the Blue Jays farm system, and made his Major League Baseball debut on April 28, 1993, as a starting pitcher against the Kansas City Royals.

On May 21, Brow earned his first career save, pitching 0.2 innings of scoreless baseball in a 9–7 win over the Cleveland Indians.

Brow began the 1998 season with the Diamondbacks, and pitched an inning in their inaugural game on March 31, allowing a run in a 9–2 loss to the Colorado Rockies.

In 1999, Brow played with the Edmonton Trappers of the Pacific Coast League, the Anaheim Angels' Triple-A affiliate, before retiring.