The Welshman came off the bench for the Red Devils in the clash and netted the team's fourth goal in an emphatic 4-0 win over the London club. It was evident how much it meant to James, and he was clearly emotional during the celebrations.
After the match, the 21-year-old spoke about his dad, who died in May, per Alex Milne of the Daily Mirror.
"Amazing really," he said. "It would have been amazing for him to be here today, but he's not, and I dedicate that goal to him. I scored the wining penalty in Cardiff last week, which was amazing, to be in Wales as well. To score on my debut here, you couldn't write it."
The winger posted the following message on Twitter after his memorable debut:
Alex Shaw of ESPN commented on the emotional scenes after James found the back of the net:
James was the only attacking signing made by United in the summer, and while he's not expected to be a first-team regular in his debut season at the club, he showcased tremendous promise on Sunday.
The Wales star was a constant threat on the counter-attack and showcased wonderful balance to squirm away from N'Golo Kante in one instance, resulting in a yellow card for the Chelsea midfielder.
United manager Ole Gunnar Solskjaer praised James following his exciting cameo:
It was the gloss on a fine opening day for the Red Devils, as they punished Chelsea with some ruthless attacking in the second period.
Marcus Rashford put United ahead from the penalty spot in the first half, with the Blues rattling the woodwork either side of that goal. After the break, United tore into Chelsea on the counter, with Anthony Martial, Rashford and then James all getting on the scoresheet.
If the Red Devils continue to play in this style, then their rapid new winger should be a threat throughout the season.
Samuel Luckhurst of the Manchester Evening News commented on how quickly United were able to transition:
Samuel Luckhurst @samuelluckhurst
At the risk of sounding like @DAHughes_, the quickness of #mufc's goals were striking: 16 seconds between Maguire's challenge and Martial's goal. Four seconds between Pogba's pass and Rashford's goal. Nine seconds between Pogba receiving Martial's lay-off and James's goal.
Of the three major summer acquisitions made by United, the purchase of James was the most understated. However, he's been bright in pre-season and after getting off the mark for his new club, will be bursting with confidence.
The Red Devils travel to Wolverhampton Wanderers next Monday for what's likely to be a challenging second fixture. It would be a surprise if James started, but Wolves will be wary of what he can offer should he emerge from the bench late on.