World number 19 Moya battled past Argentine Juan Martin Del Potro 7-5 3-6 7-5 in their third-round match, while Hewitt, ranked 20, eased to a 6-3 6-3 win over Austrian Juergen Melzer.
World number 78 Del Potro saved four match points in the third set against Moya but the Spaniard clinched victory at the fifth time of asking after a successful Hawk-Eye challenge.
The 18-year-old Argentine, who had led by an early break in the third set, let a Moya backhand go and the ball was called out by the baseline judge but the replay showed the ball was in.
Moya, champion in 2002 when he beat Hewitt in the final and at 31 the oldest player inside the world's top 20, had beaten world number three Novak Djokovic in the previous round.
On Grandstand, world number 34 Melzer broke to lead 3-2 but Hewitt hit straight back and after taking the first set, he eased to victory for a place in the last eight.
Spaniard Nicolas Almagro crushed Finn Jarkko Nieminen 6-2 6-2 to set up a likely quarter-final with top seed Roger Federer, who plays Cypriot Marcos Baghdatis later on Thursday.
