The Wellingborough professional moved into contention during the final round but eventually finished two shots off winner Brooke Henderson, who overcame an early collapse to battle back for victory.
Henderson went out in three-over-par on the front nine of the final round, allowing Hull and others to move into contention and the Northants star was only one off the pace with three holes to go.
A bogey on the 16th was followed by birdies on the last two holes as Hull closed with a round of 67 and a 15-under-par total to finish in third alongside Spain’s Carlota Ciganda, Japan’s Mao Saigo, New Zealand’s Lydia Ko and Hyo-Joo Kim of Korea.
Speaking afterwards, Hull said: “I just feel happy at the minute and I like the Europe swing.
“Today I got my driver going a lot better. I spoke to my coach right before I teed off and he gave me a few little things. It feels good to be back in contention in a major.”
Hull, who finished second at the 2016 Chevron Championship, is back in action in the Women’s Scottish Open on Thursday this week before she competes in the Women’s Open at Muirfield.