Hewitt defeated Taiwan's No.2 player Tsung-Hua Yang 6-4 6-4 6-4.
West Australian Matt Ebden will try to put Australia two-up when he meets Taiwanese No.1 Ti Chen in the second rubber of the Asia/Oceania zonal tie.
Hewitt took the edge when he broke serve for a 4-3 lead in the opening set before clinching it with an ace.
At the end of the second set, Yang took a medical time-out and appeared to be receiving treatment for a back complaint.
However, despite further issues - this time with his legs - he broke Hewitt's serve in the third set.
But the veteran Cup star broke back immediately to lead 5-4 then served out the match.
Hewitt is set to line up alongside Chris Guccione for the doubles rubber on Saturday while he and Ebden are scheduled to play again on Sunday in the reverse singles.