Tiger Woods could be back atop the world rankings by the time he heads to Royal Lytham next month for the Open Championship.

His victory at the Memorial Tournament on Sunday – where he produced what Jack Nicklaus described as "one of the most incredible shots you will ever see" – has suddenly led to a renewed belief that Woods can reclaim his place as the best player in golf.

Nicklaus was hosting the tournament and was among the first to congratulate the American as he matched his 73 PGA Tour victories, leaving only Sam Snead to catch on 82.

"He had to rub it in my face right here, didn't he?" said Nicklaus. "No, if he's going to do it, which he was obviously going to, I'd like to see it happen here. That was good."

Woods, back up to No.4 in the rankings, now hopes to move three behind Nicklaus' record of 18 majors at next week's US Open in San Francisco. He has been stuck on 14 for the past four years, but if he wins at the Olympic Club the No.1 spot – currently held by Luke Donald – will be in range again.

Woods showed a glimpse of his best form on the short 16th. With the flag down a slope and ominously close to a lake, he struck the perfect shot. "It was where he had to land it," said Nicklaus. "Unbelievable. If he hits it short the tournament's over, if he hits it long the tournament's over and he put it in the hole. I don't think under the circumstances I've ever seen a better shot."

It impressed Woods, too. He gave one of his famous fist-pumps and roars as the ball dropped and after adding another birdie at the last spoke about yet another comeback win. This was his third in six months.

"To pull off that shot at 16 was pretty sweet, but to be able to tie Jack at 73 wins – and to do it at such a young age –feels really special," he said.

The Olympic Club is his next stop – although he also went to the Masters on the back of a win and was all over the shop there – then the AT&T National at the end of the month, the Greenbrier Classic next month and then Lytham a fortnight later.

n Three-time Major champion Padraig Harrington is hoping that his love of links golf can help him win at Castle Stuart after confirming he will compete in the Aberdeen Asset Management Scottish Open this summer.

The Irishman finished tied 14th at the venue last year and he will be looking to build on a promising start to 2012, which included a share of eighth at the Masters. "I am really looking forward to getting back to Castle Stuart," he said. "There is nothing like getting back to playing links golf the week before The Open Championship."