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The 18-year-old began Saturday 11 shots off the lead at five over par, but hit nine birdies to end the day one under.
"I played aggressive and it worked for me today," Hull said.
South Korea's Park leads at five under, one shot ahead of Norway's Suzann Pettersen, China's Feng Shanshan and South Korean Ahn Sun-Ju.
Former world number one Park, who won three majors in a row in 2013, had finished one shot behind compatriot Ahn.
But Ahn's par on the final hole turned into a double bogey when she was penalised two shots for "building a stance" in a bunker on the 18th.
She said: "It's disappointing, but it's my mistake and I have to follow the rules of the game."
American overnight leader Mo Martin shot a five-over-par 77, including a double bogey on the 11th.
World number four Pettersen carded a 68 to climb into joint-second alongside Feng and Ahn.
Pettersen, 33, told BBC Two: "I'm really enjoying the course. I'm hitting the ball great and I'm confident with the putter."
But the big winner of the day was Hull, despite bogeying her opening two holes.
"I just hit fairways and hit greens and I just putted well," Hull told BBC Radio 5 live.
"The first two holes I started bogey, bogey, but I got it back from that. A great back nine and a birdie every par three made it even better."
Hull, the Ladies' European Tour's Rookie of the Year in 2013, is the best-placed home player, ahead of Dame Laura Davies, 50, who is tied in 28th at three over par.
England's Charley Hull carded a six-under-par 66, the day's best round, to move within three shots of third-round leader Inbee Park at Royal Birkdale.