Coming into this game, these teams had scored 16 goals in their previous three meetings this season and within 20 minutes gone they had added another three to their collective tally.
Arbroath opened the scoring when Craig Winter pulled down Gavin Swankie inside the box and Greig Henslee coolly converted the resulting spot kick.
However, Brechin responded with two goals in a three-minute period which saw them take the lead and control of the game.
First, a Steve Hamilton throw in fell to Charlie King and he scored with a spectacular volley from 12 yards.
Shortly afterwards, a low shot by King was turned in by Hampshire for a scrappy but deserved goal.
Brechin nearly went further ahead on 37 minutes when Graham Gibson's opportunistic header struck the bar, but after the interval they only had to wait a mere five minutes before extending their lead.
Steven Rennie gave the ball away to Emanuel Panther and he confidently curled the ball past Neil Inglis from the edge of the box.
Not content with gifting Brechin one goal in the match, Arbroath gave their visitors another easy chance to score late on when substitute Iain Diack's pass was intercepted by Hampshire who beat Inglis with a low shot.