Dominic Thiem bounced back from his opening-match loss at the ATP Finals with a gritty triumph over Rafael Nadal's replacement Pablo Carreno Busta.
World number four Thiem was beaten by Grigor Dimitrov in his first Pete Sampras Group contest and found the going tough against Carreno Busta, who stepped in for his maiden outing at the tournament after Spanish compatriot Nadal's injury-enforced withdrawal.
Thiem, whose record against Wednesday's opponent was stretched to 5-0, ultimately prevailed 6-3 3-6 6-4 to reignite his hopes of reaching the last four, while Carreno Busta cannot qualify despite a resilient showing, with Dimitrov having already progressed following his win over David Goffin.
Belgian Goffin now awaits Thiem on Friday, with the victor taking on Roger Federer in the semi-finals.
Underdog Carreno Busta settled well initially, holding confidently in his first two service games to assuage any early nerves, but he was soon undone.
Having moved into a 30-0 lead in game five, a poorly executed drop shot was the catalyst for his unravelling, with an unforced error proving decisive as Thiem broke.
When Carreno Busta served to stay in the set, he fluffed his lines again, with Thiem taking the second break point after his weighty forehand was too hot to handle.
The Austrian surrendered a break-point opening early in the second set after a series of uncharacteristically sloppy shots, affording his rival some respite.
Carreno Busta dug deep at 40-0 down in the next game, suddenly coming to life on the baseline to get the better of the rallies as a miscued Thiem forehand saw him broken.
The 2017 US Open semi-finalist kept up the pressure as he continued to produce depth and power on his shots off both wings to disrupt Thiem's rhythm, with Carreno Busta moving 5-3 ahead.
A shift in the balance of power was confirmed when Thiem failed to make his opponent serve out, meaning it was Carreno Busta who took the momentum into the decider.
And yet that initiative was promptly surrendered, with Thiem emerging the more determined and focused, as evidenced by his booming forehand that Carreno Busta could only send back into the tramlines to suffer a break.
To his huge credit, Carreno Busta fought back to to level in game six and held serve in a mammoth game seven that lasted 10 minutes and saw four break points slip by for Thiem.
From there to the end it was all Thiem, though, as he emphatically held to love and then controlled consecutive baseline exchanges to move to within one game of glory.
Such a keenly contested showdown deserved a dramatic climax and Carreno Busta did put Thiem under the spotlight at 15-30 before he finally got the job done in a match that lasted over two hours.
Thiem  bt Carreno Busta 6-3 3-6 6-4
Thiem - 27/30
Carreno Busta - 22/39
Thiem - 12/2
Carreno Busta - 2/1
BREAK POINTS WON
Thiem - 4/13
Carreno Busta - 3/3
FIRST SERVE PERCENTAGE
Thiem - 52
Carreno Busta - 64
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVE
Thiem - 90/39
Carreno Busta - 61/49
Thiem - 97
Carreno Busta - 86