Former world number one Hewitt, who reached the final at Newport earlier this month but lost to France's Nicolas Mahut, rallied for a 1-6, 6-3, 6-0 victory over third-seeded Croatian Dodig.
"At the start of the match I couldn't get into it much," said Hewitt, ranked 64th in the world, adding that the 36th-ranked Dodig just didn't give him any early openings.
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