Pettersen had a one-stroke lead heading into the 18th, but bogeyed to finish at 5-under-par 67.
She barely escaped a second-place finish when Salas -- who fired course-record, 10-under 62 Saturday -- had a birdie try on the final hole just lip out.
Each finished with a 19-under 269, easily besting the tournament record by seven strokes at Ko Olina Golf Club.
On the extra hole, Salas found a water hazard with her second shot and ended up with a double bogey while Pettersen two-putted for a title-winning par.
Pettersen's effort earned her an 11th career LPGA Tour title.
Ariya Jutanugarn carded a 6-under 66 to end with sole possession of third place at minus-15.
Sharing fourth two shots further back were world No. 1 Inbee Park (67) and I.K. Kim (65).