The 18-year-old cut inside from the left and curled a sublime finish past goalkeeper Mattijs Branderhorst in the 3-1 victory at the Amsterdam ArenA.
It was Kluivert's fifth goal of an impressive Eredivisie campaign, with his form prompting speculation over a possible move to United in January.
Manager Jose Mourinho is said to be an admirer of the left winger, who is the son of former Barcelona and Netherlands striker Patrick Kluivert, and is ready to sign him as early as next month due to concerns over his own side's lack of cutting edge in attack.
Kluivert's goal came less than 24 hours after United conceded an injury-time equaliser to draw 2-2 with 10-man Leicester City, having fought back from a goal down to go 2-1 up in the second half.
After the match, Mourinho blasted his players for a "childish" performance, during which Anthony Martial and Marcus Rashford – who have battled for a starting spot on the left of the attack this term – both missed one-on-one chances, while Jesse Lingard hit the post with the goal gaping.
Kasper Dolberg and David Neres were also on target for Ajax, whose win saw them close back to within five points of league leaders PSV.
Check out his stunning strike in the video above...