ST. ANDREWS, Scotland — Splashed with champagne, Lorena Ochoa was certain her first major victory would come at the home of golf. She completed a runaway fourstroke victory in the Women’s British Open yesterday following a 1-over-par 74. After hugging her caddie and getting doused with bubbly by her father, the top-ranked Mexican reflected on what she had done.

“It’s a long way, 24 majors, and finally I have this [trophy] here, and I think it’s for a reason and I couldn’t be more happy,” she said. “I believed I would win this tournament Monday, when I started practicing.”

Ochoa, who tied for second at the U.S. Women’s Open a month ago, had been banging on the door of a major victory for a while. This was her fourth victory of the year to go with the six she collected last year. During those 24 months, she was runner-up 10 times.

“This is the most special round of golf I ever played,” said Ochoa, who led the tournament from the ninth hole of her opening-round 67. “Hopefully this is the first of many [majors] to come.”

Ochoa, who passed $2 million in earnings this year and has a million more than anyone else, made history on all sorts of fronts. She won the first women’s professional tournament to be staged at St. Andrews, home of the exclusively male Royal & Ancient Club. And she became the first player to win her first major at St. Andrews since Tony Lema’s triumph in the men’s British Open in 1964.

Although the drought in the majors was becoming a talking point, she didn’t let it worry her.

“I accepted it all because I didn’t win,” she said. “There’s no more to say: Being at St. Andrews to make history, it’s going to be there for the rest of my life.”

She finished with a 5-under 287 total, four strokes better than Jee Young Lee (71) and Maria Hjorth (71). Reilley Rankin (71) was another stroke back at par.

Annika Sorenstam, who shared third entering the final round, finished at 296 after a 76 that included a 7 at the 17th Road Hole. In teeming rain that made scoring difficult from mid-afternoon, Sorenstam felt her foot slip on the grass and she sliced her tee shot so far right it almost struck the Old Course Hotel.

“It’s just not coming together,” she said. “This is one of those weeks when I am close, but sometimes close is not good enough.” Sorenstam, a 10-time major champion beset by neck and back injuries, saluted Ochoa.

“Everybody knows she is a fantastic player. She has matured a lot as a player. I think a major was just a matter of time.”