Max Purcell shapes as a danger man to avoid at the US Open after continuing his magnificent American hard-court run in North Carolina.

Purcell tamed big-serving Dutchman Tallon Griekspoor in two tiebreakers to advance to the quarter-finals of the Winston-Salem Open with a 7-6 (7-4) 7-6 (7-2) third-round win on Thursday (AEST).

Griekspoor had shot up to 25th in the world after reaching the final in Washington last month but learnt like so many other big names in recent times that Purcell is a fast-emerging force to be reckoned with.

Australia's 2022 Wimbledon doubles champion out-aced Griekspoor 11 to eight and, tellingly, committed a meagre 15 unforced errors off the ground during a tight encounter that stretched almost two hours.

"The courts are quite fast so it's helping me with my aggressive tennis, coming forward to the net," Purcell said.

"It's been hard to keep the ball in the court with the lively conditions and I feel I've done a good job on return to make them play that one extra ball.

"Trying to hold quickly and then straight away put pressure on them to hold their serve is working in my favour."

Purcell's reward for a 10th win from his past 12 outings is not only a last-eight crack at Jiri Lehecka, after the Czech's 6-3 3-6 6-4 victory over German Dominik Koepfer, but also yet another career-high ranking next week.

He arrived at Winston-Salem ranked 47th after downing triple grand slam champion Stan Wawrinka and world No.7 Casper Ruud en route to his maiden ATP Masters 1000 quarter-final last week in Cincinnati.

Purcell now sits 43rd in the live ATP standings and will gatecrash the world's top 40 if he wins his next match.

As world No.1 Carlos Alcaraz will testify after needing three sets to see off Purcell in Cincy, Purcell will have the seeds looking on anxiously when the US Open draw takes place on Friday morning (AEST).

While Purcell marched on, fellow Australian Aleksandar Vukic's run is over following a 4-6 6-4 6-4 third-round loss to Argentine Sebastian Baez.