Donald stood 130th in the world at the start of last year, but now he is up to 13th after a brilliant three-week spell in which he also came joint second in the Players Championship in Florida.

“That’s a great performance – I am very happy with that,” said the 27-year-old after playing the last eight holes in six under with two eagles and two birdies.

“I think I’ll be back next with confidence high. If we get good weather and I can play when the course is running I think it suits me.

“After I double-bogeyed the 10th the motto was ’never give up’. I chipped in at the 11th, holed from about 20 feet on 13, chipped in again at the 15th and on 16 must have been close to a one.”

Donald did indeed just miss the hole in one achieved soon afterwards by Trevor Immelman, but holed from three feet and after driving into the trees on the last he chopped out, then struck an eight-iron to seven feet and saved par.

Only nine others, including Thomas Bjorn last week, have eagled the 13th and 15th in the same round.

Joint second after an opening 68, Donald then had a desperately disappointing 77 but came back with two 69s.

“You can always wonder ’what if?’, but if someone had given me three rounds in the 60s on my debut I’d have taken it.”

Donald’s next two appearances also count towards the European Order of Merit. After a week off he goes to China for the Johnnie Walker Classic and BMW Asian Open.

At least he will if his visa arrives. “It’s on the way apparently,” he said.

The run of majors without a European winner has nevertheless now grown to 22 - all the way back to Paul Lawrie’s Open victory at Carnoustie in 1999.

But Donald was not the only success story. Another debutant, David Howell, earned a place in next year’s Masters as well by finishing joint 11th.

Howell, with no previous top 30s in America and with only three halfway cuts made in nine earlier majors (seven Opens, one US Open and one US PGA), shared top spot with Donald and Chris DiMarco going into the weekend.

He struggled to a third round 76 playing with Tiger Woods, but then shot 69 as well, a hat-trick of birdies from the 14th taking him into the top 16 who are invited next April.

Howell said: “I’m very pleased – my best finish in America, my best finish in a major. And I’m back next year. Brilliant. I feel like I’ve had a few years of experience in one week.”

He sank a bunker shot for an eagle at the second – the only one there all week - and holed what he called an “impossible flop shot” for par on the 10th.

Howell refused to blame the intimidation of Woods for his third-round problems.

“I don’t know that what Tiger was doing really affected me – it’s better when someone is playing well with you,” he commented. “I said to my caddie that we hadn’t had a great day, but what an event to partner Tiger in.

“He is lovely to play with. He plays fantastic golf, but he still hit some poor shots and managed to hit miraculous ones afterwards.”