The 32-year-old former world number four took advantage of some ragged play by his 69th ranked opponent to take the first set with ease on the slick grass courts.
The second set was much tighter after the players traded service breaks in the first two games as Henman's lack of confidence betrayed him at times.
He had enough experience to edge the tiebreak and clinch a morale-boosting victory just six days before the start of Wimbledon where he has been a semi-finalist four times.
In other play, dangerous Croatian seventh seed Ivo Karlovic banged down 10 aces on his way to a 6-3, 7-6 defeat of Swiss Stanislas Wawrinka and Frenchman Arnaud Clement, seeded eight, beat Swede Thomas Johansson 7-5, 6-2.
