But it hasn't been easy.
After Djokovic struggled against big-serving Milos Raonic on Tuesday, Murray needed to be at his resilient best to see off the flashy Japanese shot-maker Kei Nishikori 6-7 (9) 6-4 6-4 in a record three hours, 20 minutes: It was the longest three-set match in tournament history, surpassing the 3:12 Murray spent on court against Rafael Nadal in 2010.
Murray recorded his 21st consecutive victory Wednesday in London and turned the tables on Japan's Nishikori -- who had defeated the Scot in a similarly pulsating contest at the US Open in September.
"Nishikori was dictating almost all of the rallies today," Murray told reporters after taking an ice bath to aid his recovery. "He moves the ball around extremely well, better than maybe anyone."
Murray hasn't officially joined Djokovic in the last four at the World Tour Finals because Stan Wawrinka beat Marin Cilic 7-6 (3) 7-6 (3) in the late match in the John McEnroe group. However he is almost there.
While he will of course be content -- and relieved -- to prevail in what was the most entertaining contest so far this week, the length of the slugfest could have a knock-on effect on Murray as he tries to fend off Djokovic and secure the year-end No. 1 ranking.
Beginning his campaign at the World Tour Finals a day later than Djokovic, Murray won't benefit from a day off between the round-robin stage and the semifinals should he progress.
If Djokovic claims the title -- he is the four-time defending champion -- the Serb would end Murray's brief stint atop the rankings.
Tennis fans are buzzing about the prospect of Murray and Djokovic playing in Sunday's final and Murray admits it would make for a grand finale indeed.
"I think for the tournament and stuff, for everyone interested in tennis, that would probably be the perfect way to finish the year," Murray said.
The first set alone between the world No. 5 and Murray lasted 85 minutes, with Murray temporarily fending off a set point at 5-6 in the tiebreak with a brilliant, lunging backhand winner on what appeared to be a simple put away at the net for the 2014 US Open finalist.
Murray actually held the first set point, erring on a forehand prior to the tiebreak when leading 6-5.
But on Nishikori's fifth set point, Murray sent a forehand wide to drop only his fifth set during the imposing winning streak.
Never averse to venting to his player box, Murray was certainly in full flow Wednesday. Not only did he take out his frustration on his entourage, but he pumped his fist -- after losing points.
"I don't often do that, but today I was definitely being more sarcastic towards myself than usual," said Murray, who hadn't challenged a top-five player since losing the French Open final to Djokovic.
Murray broke in the first game of the second set, though Nishikori broke back for 4-4. How Nishikori will rue dropping serve in the ensuing game after holding game point. He'll also rue his break-point numbers -- 2-for-11, with Murray 4-for-7 -- and continuing to attempt drop shots.
While Murray produced eight aces, Nishikori didn't hit one.
Nishikori surrendered serve twice in the third set -- from 30-0 and 40-15 -- yet came back, from 1-5 to 4-5, before Murray served out the match without fuss.
"He's a tough player," said Nishikori (1-1). "Think it was great match, both of us. Also for me, played really consistent, playing with good energy.
"Well, I'm sure he's going to qualify from the group. I try to aim for the second spot."
Nishikori next battles Cilic (0-2) Friday and Murray tangles with a fellow three-time grand slam winner, Wawrinka (1-1).
"It's going to be a great match hopefully. I know I can play well here," Wawrinka, a winner over Murray at the event last year, said in an interview on court.
Djokovic tries for a third win Thursday and was due to meet the already eliminated Gael Monfils. Instead he will play Belgium's David Goffin after Monfils withdrew Wednesday citing the rib injury that kept him out of the Paris Masters.
Dominic Thiem faces Raonic, with the winner joining Djokovic in advancing from the Ivan Lendl group.