James' 17th-minute strike at the Cardiff City Stadium added to his tally of three goals at club level since he joined the Red Devils from Swansea City in the summer.
Giggs, who spent over 20 years tormenting defences from the flanks for United, has been particularly impressed with James' quick transition to a higher level. The 45-year-old told Gareth Vincent of BBC Sport Wales:
"It was a difficult one with Dan whether to rest him, but he wanted to play.
"When you are in form like his, players just want to play and keep scoring. He gets fans off their feet.
"To do what he's done at the start of the season is amazing. The next step obviously is that consistency, which he's shown so far and he needs to carry on.
"But I've got no doubts that will happen because he wants to be the best, he's a great character and a great trainer.
"He's one of those players where you know what he's going to do but you can't stop it. There are so many goals [he has scored] like that, but it's very difficult to stop because he can go either way."
It's high praise from one of the great wing wizards of the modern game. James has merited Giggs' respect after transferring his prolific club form to the international stage.
He scored as a substitute on his Premier League debut for the Red Devils, a 4-0 win over Chelsea at Old Trafford in August. James was back among the goal-scorers two matches later when he netted the equaliser in a shock 2-1 defeat at home to Crystal Palace.
James proved his early goal rush was no fluke by scoring in spectacular fashion to help earn a point at Southampton:
James has shown he can combine breathtaking pace with close control and a willingness to take shots early from distance. It's a brash way of playing, but it's already made the 21-year-old the key member of the United attack.
He's thrived while Marcus Rashford has struggled for efficiency as a finisher and Anthony Martial has dealt with injury. United boss Ole Gunnar Solskjaer, a team-mate of Giggs during their playing days, has needed James' goals after offloading the misfiring pair of Romelu Lukaku and Alexis Sanchez to Inter Milan.
Similarly, Giggs has relied on James' rapid development to help ease the burden on attacking talisman Gareth Bale. The growing importance of James for his country was underlined when he helped Wales win even though Real Madrid forward Bale was left on the bench for 50 minutes.
Bale replaced James, but the latter had offered a glimpse of an exciting future for Wales. Along with Liverpool's Harry Wilson, who is on loan to Bournemouth, James could form a potent wing duo for the Dragons for years to come.
If James becomes the consistent force Giggs anticipates he will, Wales and United will go from strength to strength.