The home favourite edged the first set before his Ukrainian opponent hit back to take the second. But the American proved too strong in the decider and went on to book his place in the second round at the International Tennis Hall of Fame & Museum.
Isner, who last year became the first top seed to win the title since the inaugural edition of the tournament in 1976, next faces face Nicolas Mahut of France.
Second seed Kei Nishikori also won through, the Japanese beating Dutchman Igor Sijsling 6-4 6-4 to set up a second-round meeting with Belgian Olivier Rocchus.
And third seed Milos Raonic of Canada saw off the challenge of Australia's Matthew Ebdon 3-6 6-3 7-5.
There was better news for Ebdon's fellow Aussie Lleyton Hewitt, the veteran easing past Canada's Vasek Pospisil 6-1 6-1, but number eight seed Gilles Muller fell at the first hurdle, losing 7-6(5) 6-7(3) 6-4 to South Africa's Izak Van der Merwe.
It was a good day for American players Sam Querrey leading the home charge with a 7-5 7-6(5) victory over fifth seed Alex Bogomolov Jr of Russia.
Joining him in the second round were compatriots Jesse Levine, Rajeev Ram and Tim Smyczek.
Levine beat Australia's Marinko Matosevic 6-2 7-6(8), Ram downed Grega Zemlja of Slovenia 6-3 6-1 and Smyczek, with possibly the upset of the round so far, ended fourth seed Denis Istomin's hopes 6-3 6-3.
Rounding off the day's action was Benjamin Becker, the German beating David Goffin of Belgium 6-4 6-3.
The tournament in Newport provides the last opportunity for grass-court practice ahead of the London Olympics.