But the home side took the lead in the 24th minute when Zola's initial shot was cleared off the line by Alan White. John Brayford curled the ball back in, and Clayton Donaldson squared for Zola to finish at the far post.
Donaldson should have doubled the lead minutes later but Liversedge came out on top in his second one-on-one. However, the striker made amends on the half-hour mark, centring for Zola whose scuffed shot fell to Grant to net at the far post again.
And four minutes later Zola headed in Ashley Westwood's cross for his second of the game.
Quakers boss Steve Staunton made three changes at half-time but the visitors still failed to make inroads on the Alex goal, Mor Diop driving their best chance wide.