Kvitova, ranked seventh in the world and seeded fifth, has struggled since capturing the Wimbledon title and the return to the Grand Slam stage proved no tonic for the 21-year-old Czech, who had 52 unforced errors.
Kvitova admitted that she wasn't yet completely comfortable carrying the mantle of Grand Slam champion into a major tournament.
"It's something new for me," she said.
She couldn't point to any particular problem in her game.
"Everything is in the head," she said. "If you are thinking on court negatively it's bad."
Dulgheru, ranked 48th in the world, advanced to a second-round clash with compatriot Monica Niculescu a 6-3, 6-3 winner over Austrian Patricia Mayr.
Dulgheru, 22, improved to 3-9 against top-10 opponents, with both of her prior victories coming on clay.
The Romanian was playing just her second singles match since Wimbledon, after which she was sidelined by knee trouble. She lost a first-round match at New Haven last week, and played only doubles at Cincinnati and New Haven.