The 6-foot-11 Karlovic had 17 aces and only two double-faults, winning 92 percent of his first-serve points during breezy conditions on the grass at Newport.
The tournament is held in conjunction with the International Tennis Hall of Fame induction ceremonies. On Saturday, Lindsay Davenport heads a class that includes coach Nick Bollettieri, executive Jane Brown Grimes and broadcaster John Barrett in the contributor category and five-time Paralympic medalist Chantal Vandierendonck.
The Hall of Fame Championships is the only tournament in North America held on grass courts.
Top-seeded John Isner is scheduled to play Tuesday. He's looking for his third title in Newport after winning in 2011-12.
The 35-year old Karlovic, a quarterfinalist in Newport last year, had first serves clocked in the 118-123 mph range in windy conditions.
"You must always adjust with the toss, and I was able to," he said.
After Karlovic went up 5-2 with his second ace of the tiebreaker, Ginepri, a 2003 Newport champion, hit a forehand return into the net and followed with a backhand that sailed wide.
The 31st-ranked Karlovic broke serve in the second and final games of the last set.
"It's always difficult on grass courts," he said. "I was a little lucky on the tiebreak, and I was able to return better and break him twice."
In other first-round play, 2009 Newport champion and American Rajeev Ram ousted Australian Matthew Ebden, 6-2, 7-5. American Donald Young, the No. 5 seed, was upset by Samuel Groth of Australia 7-6 (7), 6-2.
"I've played here a lot of years," Ram said. "I don't know if I remember it being this windy."
Sixth-seeded Steve Johnson needed only 47 minutes to top wild-card entry and fellow American Clay Thompson 6-1, 6-2; Dudi Sela of Israel beat Michal Przysiezny of Poland 6-1, 7-6 (2); Japan's Tatsuma Ito beat American Mitchell Krueger 7-6 (7), 6-1; and Malek Jaziri of Tunisa defeated Ricardas Berankis of Lithuania 7-5, 6-3.