Kim came into Sunday's play at the Evian Resort Golf Club leading Australian Webb by one shot, and a final round of 68 was good enough to see the former clinch the title.
The latter stages were full of drama, with Webb seemingly in position to complete a career grand slam before a bogey on the 18th allowed Kim to take the glory.
Webb, 39, has previously won all of the other major titles in women's golf, with the last of her successes coming in the Kraft Nabisco Championship eight years ago.
With the Evian Championship having been added to the list of majors on the LPGA Tour last year, Webb was in line to complete the set as she headed down the last hole a shot clear.
Kim had allowed Webb to gain the initiative when she bogeyed the 16th, but Webb's approach shot at 18 left her struggling to make par.
The pressure was piled on by Kim holing her birdie putt from 12 feet, leaving Webb needing to sink an effort from similar range just to force a play-off.
She was unable to do so, ensuring Kim took the spoils.