Darwin Núñez struck from Benfica's only shot on target in Amsterdam as the Portuguese side booked a last-eight spot.
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Darwin Núñez's late header took Benfica through to the UEFA Champions League quarter-finals with a 3-2 aggregate win after a battling defensive display in Amsterdam.
6' Haller effort ruled out for offside
36' Gravenberch shot tipped over
77' Darwin heads in only goal
Match in brief: Darwin swoops to conquer
Much like the teams' meeting in Lisbon, the first half was all Ajax. Antony menaced down the right, Dušan Tadić schemed on the left and Ryan Gravenberch gracefully roamed the middle with all the unencumbered ease of a man wearing velvet slippers. Yet for all their dominance, the hosts reached half-time with nothing to show for it.
Soualiho Meïté came on to interrupt Ajax's flow, and Benfica kept the Dutch side at arm's length with some comfort until they won a free-kick near the corner flag with 13 minutes left. Álex Grimaldo swung it in and Darwin rose majestically above his marker and past the onrushing André Onana to send the Eagles through.
PlayStation® Player of the Match: Darwin Núñez (Benfica)
"He scored the all-important goal, worked hard for the team and endeavoured to cause problems for the Ajax defence. He showed real leadership throughout."
UEFA Technical Observer panel
Derek Brookman, Ajax reporter
Once again Ajax's home curse in the Champions League knockout phase continues. It's now 26 years since they last won a springtime match in Amsterdam in this competition. For the vast majority of the game they looked in control, but a misjudgment by Onana allowed Darwin to head in the only goal. All in all, Erik ten Hag's men simply didn't create enough openings; Benfica defended magnificently.
Carlos Machado, Benfica reporter
They did it! Nélson Verissimo did his homework on Ajax and, for all of their possession, Benfica managed to stop Ajax from creating any clear-cut chances. The Eagles were compact and one shot on target was all they needed to make it through.
Darwin Núñez, Benfica forward: "We knew we were going to suffer and we did. We had to enjoy it when we had the ball. I am tired. We all ran a lot."
Dušan Tadić, Ajax captain: "We were the better team. Benfica did nothing, except for one free-kick. We wanted to dominate, and we did, but then in one moment... unbelievable."
Julien Weigl, Benfica midfielder: "I'm exhausted, but very happy. We had to fight, run and take our chances. The only thing that matters is that we made it through."
Fernando Meira, Eleven
"A great victory for Benfica and Portuguese football. Benfica were great, especially at the back."
Erik ten Hag, Ajax coach: "Our positional play was excellent. We were very good on the ball. Only the creativity was lacking. It's bitter that one lapse in concentration and you're eliminated."
- Benfica are through to the quarter-finals for the first time since 2015/16. The Eagles have not advanced beyond the last eight since finishing runners-up in 1990.
- This was only Benfica's second win in 17 against Dutch clubs (W8 D7), and their second victory in 15 against all opposition away from home in the Champions League.
- Ajax have not won a home game in the Champions League knockout stages since 1996. They have since drawn four and lost five.
Alejandro Grimaldo – 10
Darwin Núñez – 9
Gilberto – 7
Nicolás Otamendi – 7
Jan Vertonghen – 7
Ajax: Onana; Mazraoui, Timber (Kudus 90+6), Martínez, Blind; Edson Álvarez (Brobbey 81), Berghuis (Klaassen 81), Gravenberch; Antony, Haller, Tadić
Benfica: Vlachodimos; Gilberto (Lázaro 90+1), Otamendi, Vertonghen, Grimaldo; Weigl, Taarabt (Meite 46); Everton (Yaremchuk 72), Gonçalo Ramos (Paulo Bernardo 90+1), Rafa Silva, Darwin Núñez (Diogo Gonçalves 81)