Lee Westwood finally made the last 16 of the Accenture Match Play Championship at the 12th attempt thanks to a solid victory over Robert Karlsson on Thursday.
Needing to win the title on Sunday to regain the world number one spot from the already-departed Luke Donald, the 38-year-old third seed saw off Karlsson 3&2 in the second round at Dove Mountain near Tucson.
And Westwood does not have to face Tiger Woods to make further progress.
The three-time winner missed a six-foot birdie putt on the last and went out to fellow American Nick Watney - the man who has defeated Westwood the last two years.
Through to the third round as well are Rory McIlroy, also with a chance to go to number one by winning, and Scots Paul Lawrie and Martin Laird, who now go head-to-head for a quarter-final place.
Uncharted territory
"What's going on? This is uncharted territory for me," said Westwood. "I played very well apart from one real schoolboy mental error. Now I've got a chance to get revenge."
Six under par in defeating Nicolas Colsaerts on Wednesday, he won four of the first six holes against Karlsson but had to go far further than seemed likely when he moved five clear at the 10th.
Without a bogey in his first 27 holes, the Worksop golfer suddenly made a mess of the long 11th and then saw the Ryder Cup Swede chip in for eagle at the 583-yard 13th.
Westwood was in the desert scrub again off the tee at the driveable 15th and Karlsson did not even have to putt to be only two down.
But a par on the short next was good enough when Karlsson failed to get up and down from sand and Westwood then had to wait to see if it was Woods he faced for a place in the quarter-finals.
For the second day running Woods was involved in a tight encounter. After edging out Spain's Gonzalo Fernandez-Castano on the final green, Woods trailed Watney by two with three to play but took the 16th with a par.
After missing a chance to take it into sudden death, however, he said: "Something I was fighting all day was blocking my putts and I blocked that one."
It is the fourth year in a row that he will not be in the Friday action. He lost his opening match to Thomas Bjorn last year, did not play in 2010 and went out to Tim Clark in the second round the previous season.
McIlroy silences Hansen
McIlroy overcame Dane Anders Hansen on the 16th, while Lawrie followed up his first-round victory over England's Justin Rose by taking out 20-year-old Japanese star Ryo Ishikawa, again on the final green.
Laird got the better of 18-year-old Italian Matteo Manassero 2&1 - and had no fewer than eight birdies in the process.
"I needed all of them. That was a great match," said the US-based Laird. "That's as good as I've played in a while."
A quarter-finalist on his debut in the event 12 years ago - he was Open champion at the time, of course - Lawrie is making his first appearance since 2003.
Winner of the Qatar Masters earlier this month and on course for a return to the Ryder Cup side after a 13-year gap, the 43-year-old from Aberdeen was one ahead on three separate occasions before he finally got into a two-up lead when Ishikawa bogeyed the ninth.
His opponent refused to let him get away, though, and Lawrie's bogey on the 17th meant it went the distance. Ishikawa had a 15-foot chance to take it into extra holes, but missed.
Lawrie told Sky Sports: "I'm looking forward to tomorrow. The positive is that I'm hitting the ball good, but I'm struggling a bit with the blade (putter)."
England's Robert Rock failed to repeat his performance against world number eight Adam Scott, going down 3&2 to American Mark Wilson.
The biggest win of the week so far came from American Dustin Johnson, who after coming from three down to defeat Ryder Cup team-mate Jim Furyk thumped Italian Francesco Molinari 7&5.
Steve Stricker, another of the home contingent and winner in Australia in 2001, was in danger of going out to South African Louis Oosthuizen on his 45th birthday.
But Stricker, behind for much of the day, sank a 20-foot birdie putt on the last and then saw the 2010 Open champion miss from 13 feet.
Ernie Els, having hammered Donald 5&4, was on the receiving end of the same scoreline against Swede Peter Hanson - a big blow to his hopes of qualifying for the Masters in April.
Els will remain outside the world's top 50, but has until the end of next month to get there and earn a place at Augusta.
