Ole Gunnar Solskjaer's side were cruising by the time James entered the fray, with Marcus Rashford having scored from the penalty spot in the first half to put the home team in front, but two quick-fire goals just after the hour mark, first from Anthony Martial and then a second from Rashford, put the match beyond Chelsea.
James entered the match in the 75th minute, taking the place of Andreas Pereira, and it didn't take the youngster long to make his mark.
Paul Pogba played provider, dashing out of midfield and had looked to be in on goal before cutting the ball back near the top of the box. The slick pass split two Chelsea defenders, and James found himself in the enviable position of being in front of Kepa's goal.
A slight bobble gave Chelsea's Emerson time to recover a bit, but James managed to get a shot away which took a slight deflection off the Blues defender before finding the net.
Having joined United in a £15 million ($19m) move this summer from Swansea City, the 21-year-old is already making a bit of a name for himself.
“You couldn’t write it,” the Welshman told MUTV at the time.
“Amazing. We’ve come from behind, today was a different test."
He has now recorded his first goal for the club in a competitive match as his star continues to rise at the Theatre of Dreams.
It was just the fifth league goal for James in his professional career, having scored four times for Swansea, and, amazingly, all five of those strikes have come in home matches.
"I don't think you can sum up how it feels, to come on and score on my debut," he said on Match of the Day. "I've dreamt of that. Ole said to be ready to come on. He said to go and enjoy yourself.
"Everything we have been doing in pre-season we have done today - high press and winning the ball back. We were keeping it well, even at 3-0 and 4-0. It sets us up well going in to next week."
James could get the chance to add to his growing legacy with the club returning to the pitch next Monday against Wolves, looking to continue their fine start to the new campaign.