The 29-year-old Hewitt's victory was his 27th on the ATP Tour but only his first since 2007.
Hewitt jumped ahead in the first set and appeared to be heading for an easy win but Odesnik fought back and got to within 6-5 in the second set.
The South African-born U.S. player had never before played in an ATP tournament final.
"It's always nice to get back in the winner's circle," Hewitt said. "This is what the hard work is for, to play weeks like this and to have this kind of feeling at the end of them."