Murray fired an ace out wide on match point to overcome Argentina's Tomas Etcheverry 6-7(5) 6-1 6-4 in the latest in a string of impressive comebacks for the ageless Scot.
"I've been fighting my hardest. I really want to make the most of these last years that I've got," Murray said on court after the three-hour and 12-minute contest.
"I've managed to fight through some brutal matches. It's been incredible really.
"I don't want it to stop. I know it will at some stage but while it's going like this, might as well enjoy it."
Murray dropped the tight first set and frustration with his play and some of the calls made by the electric line calling system threatened to boil over.
But like he has so many times in his career, he roared back with help from his ferocious forehand in the second set to force a decider.
The match then hinged on a marathon game at 4-4 in the third where Murray executed a perfectly placed half-volley winner that sent Etcheverry running off the court in pursuit.
Murray's sixth ace of the match sealed the win as he improved to 7-0 in deciding set matches this year.
Next up is a meeting with Spain's Pablo Carreno Busta in the second round on Saturday and three-time Grand Slam champion Murray said he is as hungry as ever.
"I still feel extremely motivated, I still enjoy the competition and all the work that goes into it," he said.
Earlier in the day Murray's compatriot Raducanu battled back from a break down in both sets to beat Danka Kovinic 6-2 6-3 and get revenge on the Montenegrin who beat her at the 2022 Australian Open.
No one was quite sure what to expect from the Briton coming into the WTA 1000 tournament in the Southern California desert, even whether she would actually take the court.
The wrist injury that forced her to shut down her season early last year has reportedly been flaring up again and after she withdrew from a pre-tournament exhibition event, it appeared she might not compete at all.
But she walked on to the sun-soaked showpiece court to a loud ovation and after going 2-0 down, began to find the range with her forehand and sealed the 33-minute first set with a second service ace.
The story repeated in the second set where she again fell behind 2-0 before recovering to advance to the second round, where she will face Poland's Magda Linette.
"I'm happy I stuck in," Raducanu said in an on-court interview.
"Being a break down is difficult of course but I think mentally I just took it a point at a time."
She said she relished playing on what she called one of her favorite courts.
"I'm just so happy to have got through and hopefully play another match in front of you guys," she said.
In other first round action, Switzerland's three-time Grand Slam champion Stan Wawrinka made a winning return to the tournament after a four year absence and Australia's Thanasi Kokkinakis advanced to set up a meeting with top seed Carlos Alcaraz of Spain.
On the women's side American Madison Brengle and Czechs Marketa Vondrousova and Karolina Muchova were among those who reached the second round.
The 32 seeded players on the men's and women's side enjoy first round byes at the Masters and WTA 1000 event.
