Rory McIlroy in pursuit of US Open leader Bryson DeChambeau

Rory McIlroy was in the hunt (Matt York/AP) (AP)

Rory McIlroy had an overdue fifth major title within his sights after eating into his overnight deficit in the final round of the US Open at Pinehurst.

Starting the day three shots behind Bryson DeChambeau, McIlroy made the ideal start with a birdie from 20 feet on the first and found himself just a shot behind when DeChambeau bogeyed the fourth.

McIlroy was then unfortunate to drop a shot on the par-five fifth after what looked an excellent approach ran off the sloping green into one of the native areas.

From a poor lie, McIlroy chipped into the bunker in front of him and narrowly failed to hole a 20-foot par putt.

McIlroy closed the gap again with a birdie from 15 feet on the ninth, but DeChambeau kept his nose in front with par from a similar distance on the eighth.

Playing alongside McIlroy, Patrick Cantlay was two shots off the lead after narrowly failing to match McIlroy’s birdie on the ninth.

Former champion Martin Kaymer had earlier showed what was possible – both good and bad – in the final round.

Ten years after leading from start to finish and winning by eight shots at Pinehurst, Kaymer carded a closing 73 to finish 13 over par.

The former world number one birdied the first, fifth, 10th and 13th – where a forward tee had brought the green into range – but also made a double bogey on the ninth and a quadruple-bogey eight on the 14th.

“I think it’s very fair, I think you can shoot two or three under par,” Kaymer told the PA news agency.

“You do have some tricky pins but you know that. You have to play away from flags quite often so you rely on a lot of putts inside 10 feet because you will miss the odd green.”

Asked about his problems on the 14th, Kaymer added: “I hit a decent bunker shot which just trickled over (the green) and then it didn’t really matter if I finished 50th or 60th so I tried to hit a really nice, cute pitch shot and it came up short twice, but it was a fun week. I enjoyed the challenge.

“Regardless of if it’s Pinehurst or not, I like that feeling of playing well in a major, having a chance.

“Obviously I’m still quite far away from being in contention but to experience Pinehurst again with the crowds and the memories, it was beautiful.”

Kaymer played a practice round with Rory McIlroy earlier in the week and was also alongside the Northern Irishman for the first two rounds of the 2014 US PGA at Valhalla, McIlroy’s most recent major win.

“He plays the same way he did back then, winning is just so difficult,” Kaymer said of McIlroy.

“He came close so many times, I think it’s just a matter of making those clutch putts on the back nine.

“We all know he’s good enough but you do need a little bit of luck as well. When people say he hasn’t won for 10 years, that’s quite unfair towards him.

“It’s very difficult winning major championships and he finished many times in the top 10 which is also a good achievement. I think it’s just a matter of time.”