Manchester United were beaten for the second time in as many games as Feyenoord won Thursday's Europa League contest 1-0 at De Kuip.
In a lacklustre encounter in Rotterdam it was the hosts that earned a big three points through Vilhena's 79th minute goal, despite suspicions of offside in the build-up.
The defeat marks further disappointment for United after last weekend's 2-1 derby defeat to Manchester City, which marked their first competitive loss under Jose Mourinho.
The Portuguese made eight changes from that loss and, despite boasting the likes of Paul Pogba, Anthony Martial and Marcus Rashford, the visitors failed to click and seldom troubled the hosts' defence.
And they were duly punished by a Feyenoord side flying this season, with Giovanni van Bronckhorst's men sitting top of the Eredivisie having won five from five.
After a solid start to the Mourinho era, United are now under pressure for the first time and will seek a swift return to winning ways against Watford in the Premier League on Sunday.
Feyenoord saw plenty of the ball early doors and David de Gea had to get down low to hold onto a bending effort from Steven Berghuis.
United's play was scrappy at times with lone striker Rashford guilty of a few misplaced passes and too often running into dead ends, while their midfield struggled for fluency.
The visitors missed the best chance of the half, though, when Matteo Darmian teed up Martial on the edge of the area, only for the France forward to fizz a half-volley past the right-hand post when he should have at least hit the target.
But it was Feyenoord that finished the half stronger and Jens Toornstra disappointingly slashed wide from the right of the penalty area.
United initially started the second half with more intent, but soon reverted back to the more pedestrian tempo adopted in the opening 45 minutes.
Feyenoord continued to probe and Karim El Ahmadi flashed a 25-yard effort wide of the left-hand post.
Pogba, who was largely ineffective, tried his luck from a similar distance but was also unsuccessful.
Mourinho had seen enough and brought on Zlatan Ibrahimovic in a bid to add some spark to United's attack.
The Sweden star almost made a swift impact from an Ashley Young free-kick, but just failed to make clean contact with the header on the stretch.
And United were undone in the 79th minute as the noise levels in De Kuip rose significantly.
Nicolai Jorgensen may have been just offside when he was sent clear down the right and he cut back for Vilhena to provide a cool side-footed finish from just inside the penalty area that De Gea could not keep out.
The goal finally sparked a response from United and they piled forward in the closing stages but, despite a well-hit long-range free-kick from Ibrahimovic that was saved by Brad Jones, it proved a fruitless search for an equaliser.