The surprise win was a welcome tonic for Feyenoord, who came into the match in disarray after axing manager Brian Priske less than 48 hours before the game.

"These evenings are why we do this," said a jubilant Feyenoord captain Quinten Timber.

"De Kuip was on it again. We were on it. On to next week," he said.

In driving Rotterdam rain, the crowd had barely settled from the raucous pre-match singalong when the hosts took the lead thanks to Maignan's inexplicable howler.

With only three minutes on the clock, Feyenoord's Brazilian winger Igor Paixao cut in from the left and fired a speculative shot along the sodden turf.

The strike should never even have troubled the French international keeper but he somehow failed to collect it cleanly and it ricocheted off his body into the top corner.

Buoyed by a feverish atmosphere inside De Kuip, the Dutch side had the better of the opening exchanges, winning most of the 50-50 balls and adapting well to the slow surface.

Seven-time European champions AC Milan in contrast were sloppy and could not match the work rate of the home side.

Paixao was causing chaos with scything runs down the left-wing and saw a curling shot glance off the bar just before the break, with Maignan well beaten.

Defensively solid and Paixao in particular dangerous in attack, the unfancied hosts were good value for their 1-0 half-time lead, showing interim boss Pascal Bosschaart plenty of heart and commitment.

- 'We did it again' -

The second half lacked clear-cut chances until the 71st minute when the outstanding Paixao dispossessed England's Kyle Walker and nearly scored with a lob from the halfway line.

Milan had one of their first meaningful shots on target when substitute Samuel Chukwueze tried his luck from distance but could only find Feyenoord keeper Timon Wellenreuther.

The one goal proved enough on the night for Feyenoord to take the upper hand back to Milan, who will need to show far more penetration in the return leg at the San Siro on February 18.

The match was a disappointing homecoming for AC Milan's new striker Santiago Gimenez, who had only left De Kuip two weeks earlier after two and a half years and 65 goals in 105 appearances.

The visitors lacked bite up front in general and Gimenez was largely anonymous until he was substituted on 82 minutes, receiving a warm ovation from the Feyenoord fans.

AC Milan's Dutch midfielder Tijjani Reijnders said his side "lacked aggression" in the cauldron of De Kuip.

"Both in attack and defence, it was not enough and then you simply come up short," he said.

"We have to be much more consistent."

Feyenoord will be hoping a win over AC Milan could herald the start of something special.

In the only previous European meeting between the two, the Rotterdam club took out the Italian giants in their run to their only European Cup title, in 1969-1970.

Awaiting the winner will be a clash with either Inter Milan or Arsenal.

"There's a reason we're where we are now, because we've played many good matches in the Champions League," said Timber.

"And we did it again tonight."