Kerr ended the third round with a two-shot lead over Pettersen and Stacy Lewis.
After Pettersen birdied 14 and Kerr bogeyed, the Norwegian took her first lead of the day at 11-under.
Both had birdies on 15, then Kerr equaled the match at 12-under with a birdie on 16.
"I had to come up strong on the last four or five holes and I did that, made some huge putts," said Kerr.
Aria Jutanugarn and Ilhee Lee tied for third at 10-under.
Jutanugarn, the 17-year-old from Thailand, made a run for the lead with birdies on 11, 13, 14, 15 and 16. She has played in four LPGA Tour events and hasn't finished lower than fourth.
Lee won only $38,318 in her previous seven tournaments and her best finish was tied for 24th. She earned $76,327 for her third-place finish.
Angela Stanford, who started the day 7-under, finished at 9-under, the same as top-ranked American Lewis.
Like Pettersen, Lewis was two shots behind Kerr at the start of the round, but two early bogeys took her out of contention.
World No. 1 Inbee Park had four front-nine birdies and finished at 8-under in seventh place.
"Nothing would fall for me on the back nine. … I hit everything within 15 feet on the back nine, but just missed everything when I had the line," said the world's No. 1 player. "I played very good on the front nine. "
Neither of the golfers involved in last year's marathon playoff were factors this year.
Jiyai Shin, who won the playoff, finished 2-over, 14 strokes off the lead.
Paula Creamer, who had eight pars on 18 in the playoff last year, had a bogey and two pars in her first three rounds of 2013. She finally got her long-awaited birdie at the end of her final round Sunday to finish 3-under.
The Kingsmill Championship wrapped up its two-year deal with the LPGA on Sunday, and it's uncertain if the Tour will return to Williamsburg. Kingsmill has yet to find a title sponsor.
"This tournament deserves to be here and deserves to be on our schedule," Kerr said. "...Everybody loves the golf course and where it is, you know. It would be great if we could get another sponsor to step up."