Brechin attacked from the start and after three minutes Darren Smith beat two players and crossed for Kevin Byers to drive over. On eight minutes Craig Winter was next to go close with a drive which was just off target.
Clyde went close on nine minutes when Joe Miller had the ball in the net from a Chris Higgins cross but was given off side. On 16 minutes an Eddie Malone cross from the left and Miller was denied by Craig Nelson.
Back came Brechin and on 17 minutes David White had a volley saved by keeper Peter Cherry. Brechin opened the scoring on 20 minutes when Smith crossed for Hampshire to prod the ball home.
Brechin went close again on 27 minutes when White volleyed inches over. Moments later Craig Winter headed the ball down and Charlie King was denied by Cherry.
Brechin stretched the lead on 55 minutes when King crossed for Hampshire to score his second goal with the aid of a deflection.
Hampshire almost completed his hat-trick on 71 minutes when he shot inches wide after great work by King.
Brechin were reduced to ten men on 74 minutes when Craig Winter was sent off for his second booking.
The ten men made it 3-0 on 87 minutes when trail striker Chris Geddes darted clear to score.
Clyde got a consolation goal in the final minute when Craig Bryson netted from close range in a goal-mouth scramble.