Yet now they're the only two players to win the first three majors of the year. Park became the first to accomplish the feat in the modern era Sunday with her second U.S. Women's Open title.
"Trying to put my name next to hers means just so much," Park said. "I would think I would never get there; it's somewhere that I've never dreamed of. But all of a sudden, I'm there."
The world's top-ranked player finished at 8 under to win by four strokes. Her 2-over 74 in the final round was more than enough, with Sebonack's trying conditions keeping any rivals from making a run. Only three players were under par for the tournament.
Fellow South Korean I.K. Kim also shot 74 for her second runner-up finish at a major.
Zaharias won the year's first three majors in 1950 - back when there were only three. Now there are five, so Grand Slam might not quite be the right term if Park wins all of them.
Ahead by four strokes at the start of the round, Park birdied the ninth and 10th holes to extend her lead. She has won six times already this year, including three straight tournaments. Park added to another historic U.S. Women's Open victory in 2008, when she became the event's youngest champion at age 19.
"I didn't know what was going on at that time," Park said. "I played very good golf then, but I didn't know what I was playing for, and that was just my first win. It was a great championship then, but now I think I really appreciate more and I really know what this means."
So Yeon Ryu shot 72 to finish third at 1 under. South Korean players took the top three spots and have won the last five majors.
Ryu and Na Yeon Choi, the last two U.S. Women's Open champs, sprayed Park with champagne after she made her final putt on the 18th green.
With lashing wind and devilish greens, Sebonack was a classically troublesome U.S. Women's Open course. And once Park built a lead, nobody could mount a charge.
She certainly wasn't going to make enough mistakes to come back to the field. Park had just 10 bogeys and no double bogeys in four rounds.
She predicted Saturday that shooting even par in the final round would be enough, and she sure was right.
All of four players were under par Sunday - though that was still more than the third round, when only Park achieved it.
Kim birdied No. 2 to pull within three strokes; she couldn't claw closer. And when she bogeyed the fourth hole, the deficit was back to four shots.
Park bogeyed the sixth and seventh, but so did Kim.
Kim had what would have qualified as a sensational week if not for Park, finishing at least three strokes better than everyone but the player currently dominating the sport.
"You can obviously feel for someone like I.K. Kim who would be winning any other U.S. Open on this golf course if it weren't for Inbee," said seven-time major champion Karrie Webb.
This was Kim's fourth top-four finish at a U.S. Women's Open, but she's still seeking her first major title. She was a foot away last year at the Kraft Nabisco, then missed a short putt on No. 18 that would have clinched the championship and went on to lose in a playoff.
Asked if she feels she's on the verge of a major breakthrough, Kim paused for a moment then said: "Yeah, to be honest, yeah, it's time to win it."
"But I think things have to come naturally," she added, "and it's great to play with Inbee, and she's doing so well. Seeing her doing it, it just makes me want it more."
Americans Paula Creamer (72) and Angela Stanford (74) and England's Jodi Ewart Shadoff (76) tied for fourth at 1 over. Shadoff was alone in third at 3 under after the third round but opened Sunday with three straight bogeys.
Soon-to-be Oklahoma State player Casie Cathrea shot 70 on Sunday to match Shanshan Feng for the best round of the day and finish as the low amateur at 9 over. Lydia Ko, the 16-year-old New Zealander who won the Canadian Open last August to become the youngest LPGA Tour winner, was next at 11 over.
Park also became the second player to win the U.S. Women's Open after victories in her previous two tournaments. Mickey Wright did it in 1964.
The 24-year-old Park won the Kraft Nabisco and LPGA Championship for her first two major titles of the year. Up next is the Women's British Open at St. Andrews on Aug. 1-4.
The Evian Championship is Sept. 12-15. Park won the French event last year before it became a major championship.
Park contemplated the current definition of a Grand Slam.
"So I think the British Open is one I have to win," she said. "So it would be great if I could win five, but I still think four means a Grand Slam.
Laughing, she added: "I think four out of five is very big."