Rain had prevented all but three games of the match, which had been scheduled to begin on Tuesday, being played, and when it did finally get going in earnest Murray wasted little time.
Perhaps understandably, the world number four was not at his best, and he will need to improve his serve substantially if he is to go further, but a quick victory was just what the circumstances required.
Young has provided one of the stories of the tournament, the teenage prodigy written off as a flop who looks like he has finally started to fulfil his potential at the age of 22.
Victory over Stanislas Wawrinka in round two was particularly impressive and Young could take confidence from knowing he had won his only previous clash against Murray in Indian Wells in March.
That came during the Scot's post-Australian Open final slump and he freely admitted before the match that he was seeking revenge to bury the memory of one of his most disappointing losses.
All the delays seemed likely to play into the hands of the more experienced player and Murray duly won the first seven points on Thursday morning before breaking for 3-2 when Young served a double fault.
It was a tentative start from both players, with the court slow after all the rain, but Murray upped the pace with two brilliant backhands in the seventh game and secured another break when Young fired wide before polishing off the set.
The momentum stayed with him at the start of the second set, with Murray claiming his third successive break.
Young finally stopped the rot at seven games in a row but it was now a huge task for the wild card.
However, buoyed by winning a game and a sudden drop in intensity from his opponent, the 22-year-old brought up three break points.
Murray saved the first but on the second opted for an ill-advised challenge on a line call and lost the point and the game when the replay showed Young's shot was well in.
The Scot was let off the hook in a major way when, from 30-0, Young played four poor shots to hand the break back, only for Murray to serve a double fault on break point and square the set again at 3-3.
Incredibly, a fourth consecutive break followed, and then Murray, whose first-serve percentage was well below 50%, managed to hold.
Young, though, was still struggling badly, his tally of unforced errors at a prohibitive 35, and a double fault on set point handed it to Murray.
The quality was not the best but Murray played a superb running forehand to help him hold serve in the opening game of the third set.
Young's wayward forehand had been the major problem and Murray broke through again in the fourth game when the American netted a simple volley, but a backhand into the net from the world number four continued the topsy-turvy nature of the clash.
Despite his own struggles, Murray always looked capable of breaking his opponent's serve, and that was the case again in the eighth game as he moved to the brink of victory, which he completed, somewhat ironically, with an ace.