The Brit eased past France's Adrian Mannarino in straight sets to set up a tie with the 18-year-old, who claimed a 7-5 first-set victory after Murray had initially stormed into 3-0 lead.
However, Murray took the second and third sets 6-3 and 6-2 to advance to the third round, and the three-time Grand Slam winner - who defended his use of the underarm serve - labelled the encounter "brutal" after prevailing.
Speaking to Amazon, Murray said: "It was a brutal match, really tough conditions. The way I fought after losing the first set was great because I feel I should have won that first set.
"I created lots of chances but didn't take them. It would've been easy to let that slip away but I kept fighting and finished it well. The courts are painfully slow here, I was thinking about using it [the underarm serve] again in the third set.
"He changed his return position towards the end of the first, he started going further back and I was like 'just give it a go and see. I used it, it worked well and maybe I'll use it again in the future if guys are going to stand that far back and they're going to make courts like this."
Murray's third-round opponent will be world number four Alexander Zverev, who recently welcomed the ATP investigation into allegations of domestic violence made against him by ex-girlfriend Olga Sharypova. body check tags ::