It was a game that Berwick keeper Gary O'Connor may want to forget after his early blunder gave the home side the lead. O'Connor made two impressive early saves, denying Charlie King and Kevin Byers, but in the 28th minute he failed to clear a Mark Cowan back-pass, which let in Hampshire for the opener.
Berwick immediately went on the offensive, but were unable to break down the solid Brechin defence. Kevin Gordon and Gareth Hutchison both went close, late on in the first half.
Hampshire's run of luck continued into the second half, when his 54th minute long-range effort looped over O'Connor's head after taking a deflection, making it 2-0 to the home side.
Berwick looked dead and buried, but pulled one back out of nowhere. The ball fell to Mark McGarty on the edge of the Brechin area, and he unleashed an unstoppable 20-yard half-volley past the helpless Craig Nelson.
Hampshire once again proved to be the thorn in Berwick's flesh however, when he set up King, who fired convincingly home to make it 3-1. Minutes later, Cowan brought down Hampshire in the box and the on-form number 11 stepped up to score from the spot and complete the rout.