The 22-year-old Netherlands international, who made 136 appearances for Feyenoord, is the first new arrival of Erik ten Hag's tenure as United manager following his move from Ajax.
Roma's Portuguese midfielder Sergio Oliveira had an early appearance as he was substituted in for Henrikh Mkhitaryan in the 16th minute.
Feyenoord lost their third match 2-1 against Ukrainian side Shakhtar Donetsk in Group F.
With their 25th win of the season, Feyenoord are now on 79 points with two match rounds remaining.
Feyenoord now lead the table with 76 points from 31 matches, followed by Ajax (75) and PSV (69).
The win means Ajax narrowed the gap with Feyenoord on table to three points.
League leaders Feyenoord had no problems in the Rotterdam derby , thrashing Sparta 6-1 on Sunday.
