Just seven minutes after coming on, the 21-year-old winger latched onto Paul Pogba's pass and found the bottom corner, courtesy of a deflection.
He sprinted over to the corner flag to celebrate and was visibly emotional as his new teammates surrounded him.
James' father, Kevin, tragically passed away three weeks before his £15m move to United and would have been very proud.
Once United's players had parted, James paid tribute by pointing to the heavens.
James gave an interview with the Premier League after the game where he spoke about the emotions of scoring on his United debut after the passing of his father.
"Amazing really," the Welshman replied. "It would have been amazing for him to be here today, but he's not, and I dedicate that goal to him.
"I scored a winning penalty in Cardiff last week which was amazing, to be in Wales as well. To score on my debut here (Old Trafford), you couldn't write it."
Watch James' emotional interview in the video below, with his comments on his father coming at 1:15.
James also received praise from Jose Mourinho, who seemed very impressed by his, Maguire and Wan-Bissaka's contributions against Chelsea.
"For the three boys, it was fantastic," Mourinho said in the Sky Sports studio.
"Maguire Man of the Match, Wan-Bissaka very solid, very confident, and then this kid (James) comes on and in twenty minutes, he scores a goal. For these three boys, it couldn't be a better day."News Now - Sport News