One stroke short of the play-off pair were South Korea's Se Ri Pak and Americans Wendy Ward and Nancy Scranton.
The American captured her sixth career LPGA major and 24th tour title overall to join a select band of women - Pat Bradley, Patty Sheehan and Betsy King - with the most majors of any active LPGA player.
Inkster also joined Sheehan and Mickey Wright as the only women to ever defend the LPGA Championship.
"It was great," Inkster said. "I struggled coming in but I hit the shots when I had to. I'm very proud of myself."
One stroke short of the play-off pair were South Korea's Se Ri Pak and Americans Wendy Ward and Nancy Scranton.
Australia's Jane Crafter, Britain's Laura Davies and American Heather Bowie shared sixth.
While Croce charged through the field on Sunday with a joint best-of-day 68, the main challengers fell away, and even Inkster could do no better than 75, which included a three-putt at the 18th for a three-under-par 281 to send the contest into extra time.
Missed chances
Britain's Laura Davies was among those who reckoned they had thrown the title away.
The halfway leader by two, she shot 75 and 72 over the weekend and still finished just two outside the play-off.
"I should have won and am really disappointed," said Davies, a three time winner over the course - including two LPGA Championships.
In the play-off the first hole was halved in par before Inkster claimed the $140,000 top prize at the par-four tenth when Croce overshot the green.
For the 30-year-old Italian, who had never finished higher than third in seven years on the tour, it was still a great week.
"I never really thought I had a chance when I came in," she said.
"At that stage I was three behind. But this has been super for me and, hopefully, a stepping stone to better things."