The 31-year-old Hewitt seized his single break-point opportunity in the opening set and fought back again in the decider to beat a player ranked 64 places higher in the current world rankings.
Cypriot seventh seed Marcos Baghdatis advanced with the minimum of fuss, taking just 73 minutes to dispatch world number 45 David Goffin of Belgium 6-4 6-2.
Fifth seed Feliciano Lopez beat Paul-Henri Mathieu of France 7-6 (7-5) 6-7 (7-4) 6-2, and Ukraine's Sergiy Stakhovsky was comfortable 6-3 6-4 winner over Belgium's Yannick Mertens.
Japan's Go Soeda beat French qualifier Maxime Teixeira 6-3 3-6 6-3 and there were also wins for Ricardas Berankis, Jurgen Zopp, Alejandro Falla and Romanian qualifier Marius Copil.
Frenchman Gael Monfils was stunned by home favourite Patrik Rosenholm in the late match on Centre Court.
Monfils, whose recent career has been hit by injuries, went down 6-3 1-6 6-3 to the world number 436, who wrapped up victory in 78 minutes.