The British tennis star followed up Wednesday's three-set battle with Japan's Kei Nishikori
by sealing a semifinal place with a more straightforward 6-4 6-2 victory over third-ranked Stan Wawrinka.
It gave Murray a 3-0 record in his group, and sets up the possibility of a year-end No. 1 showdown with Novak Djokovic if both win on Saturday.
Wawrinka, however, exited the season-ending tournament after suffering his second round-robin defeat.
The Swiss player had won three of their past four meetings, but his inconsistency meant he couldn't match Murray's mental fortitude in a match lasting less than 90 minutes -- not even half the time the Scot spent on court against Nishikori.
However, the scoreline doesn't tell the whole story.
Wawrinka typically saves his best for the big occasion -- the 31-year-old is 3-0 vs. world No. 1s in grand slam finals and 0-19 otherwise.
Often maligned for blowing hot and cold, Wawrinka opened proceedings with a succession of ripping winners -- the first a trademark backhand down the line -- to put Murray on the back foot.
If the "Stanimal" was silenced by Nishikori earlier this week
, he was now out of his cage.
"I think I weathered the early storm a little bit," Murray admitted after the match. "Stan came out hitting a lot of winners, a lot of aces."
The sellout home crowd could have been forgiven for shifting awkwardly in their seats. Wawrinka had cut a disconsolate figure even before Monday's defeat was wrapped up; here he was quite the opposite, taking risks, pumping fists and generally playing with a far greater sense of urgency.
Murray, after all, only had to win a set to guarantee his own path to the last four, while Wawrinka -- who had just one victory, against Marin Cilic -- needed every point he could get to have a chance of progressing to the semis for the fourth year in a row.
But despite the complex qualification permutations, Murray didn't once take his foot off the gas.
"Once I got through the early part of the match, I started to create chances in most of his service games," said Murray. "I served very well myself, [and] got a lot of free points on my serve."
Wawrinka also attributed Murray's success to his consistency.
"Murray was serving really well. He didn't give me even a chance, and made me hesitate a bit with my game — when to go and when to stay back."
"That's why he's so good; that's why he's no. 1."
Even after the longest three-set match in the tournament's history, ice baths and just a single day's rest, Murray had the sheer guts to gradually wear down his opponent.
And, having taken the first set with one of his first break-point opportunities, Murray came out of the blocks quickly at the restart to break his opponent again.
Wawrinka's urgency turned to anger and desperation. When Murray broke again to open up a 4-0 lead, his opponent snapped -- taking his frustrations out on his racket -- joking after the match "if I'm going to break it, I'll do it properly."
Wawrinka may have caught the eye, hitting 29 winners to 15, but Murray won the points that mattered and made just 13 unforced errors to 27.
He will next face Canadian fourth seed Milos Raonic in a rematch of July's Wimbledon final
, where Murray claimed his third grand slam title.
Djokovic, who can reclaim the No. 1 ranking by winning the tournament for the fifth successive year, will play fifth seed Nishikori in his semifinal after topping his group with three wins.
Nishikori progressed to the last four for the first time, having won more sets than Wawrinka ahead of his final group match against Croatia's Cilic in Friday's evening session. Cilic downed Nishikori 3-6 6-2 6-3 in a repeat of the 2014 US Open final also won by the former.