Kerr sank a short putt on the second hole of the play-off for par after Pettersen bogeyed.
Kerr had begun the day with a two-shot lead, but her two-under 69 was bettered by Pettersen's 67 to force the extra holes at the River Course.
Both players had four birdies, but Kerr bogeyed the fifth and 14th holes to surrender her advantage.
Thai teenager Ariya Jutanugarn, who led going into the weekend on the back of an opening round of 64, recovered from yesterday's 73 with a round of 66 to share third place with Ilhee Lee.
Stacy Lewis, who had enjoyed a share of second overnight alongside Pettersen, could only manage a round of 70 today and dropped back into a share of fifth alongside Angela Stanford.