Promoted Alton ignored wind and rain to take the lead inside 20 seconds, with a tap-in from Elliott Pate.
The next half-hour saw several missed opportunities for Alton and a number of breakaway attacks by Andover, which fortunately were foiled by Adrian Rankin.
Then a goal from James Goulding-Stewart sent Alton in two up at half-time.
Lack of concentration led to an Andover goal two minutes after the break, but it acted as a catalyst for an outstanding second-half performance from Alton.
A second goal for Pate and two for Hugo Hammond in quick succession steadied the team and saw Andover become increasingly frustrated.
Alton’s Andrew Stratford was felled by a sliding tackle more suited to a football pitch.
Alton kept their composure and scored a superb team goal, nicely finished off by John Ardagh.
Towards the end Simon Millard produced a shot that gave the keeper no chance, then Hammond completed his hat-trick.