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.
Rafael Nadal was forced to retire with cramps while Carlos Moya defeated Novak Djokovic.
Former world number one Marat Safin was dumped out in the first round of the Cincinnati Masters on Monday, beaten 6-3 7-6 by German Nicolas Kiefer.
Serbia's Novak Djokovic produced the performance of his career to beat world number one and defending champion Roger Federer 7-6, 2-6, 7-6 to win the Montreal Masters on Sunday.
Justine Henin opened the defence of her French Open crown with a battling 6-4, 6-3 win over 20-year-old Russian Elena Vesnina on Sunday.
An ultra-confident Rafael Nadal takes his clay-court master-class to Spain this week going for a third Barcelona Open title in succession.
Former world number one Gustavo Kuerten earned his first hard court victory for 18 months when he booked a place in the round-robin section of the Las Vegas Open on Monday.
The Russian beat American wildcard Scott Oudsema 6-4, 7-6 to reach the second round on Tuesday.
The American teenager beat compatriot Paul Goldstein in the San Jose Open first round on Monday.
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