The Brewers took the lead in the 22nd minute when Alex McAllister strode forward from just inside the attacking half and left two defenders in his wake as he bore down on goal before passing the ball into the corner of the net.
The visitors equalised on 82 minutes through Troy Murray’s shot from the edge of the box.
Alton regained the lead on 88 minutes when McAllister delivered a peach of a cross that was met by the head of Jamie Hoppitt, who thumped home from six yards.
Alton manager Kevin Adair said: “We created a lot of chances – which was really pleasing – but we could have been more clinical and scored more goals.”