Two goals from Sadio Mane helped Liverpool see off Bayern Munich 3-1 at the Allianz Arena to book their spot in the Champions League quarter-finals for the second successive season.
Neither side created many clear opportunities on a wet night in Munich and both sets of players were guilty of giving away possession too easily and too often.
However, the Reds carried more of a cutting edge and took the lead in the tie in the 26th minute when Mane displayed an exquisite touch to bring down Van Dijk’s raking pass before firing into an empty net after Manuel Neuer had rushed from his goal.
Bayern now needed at least two goals and pulled one back when Joel Matip turned into his own net from close range.
However, the expectant waves of attack from the German champions never materialised after the break, and Van Dijk all but ensured Liverpool’s spot in the last eight when he powered home with a head from James Milner’s corner.
Mane capped off an excellent night for him personally when he headed in his second six minutes from time.
Elsewhere, Lionel Messi scored twice and set up two more as Barcelona reached the Champions League quarter-finals for a record 12th consecutive year with a 5-1 win over Lyon.
Barca, who drew 0-0 in the first leg, led when Messi chipped home a penalty.
Philippe Coutinho tapped into an empty net from Luis Suarez’s unselfish pass before Lucas Tousart’s volley gave Lyon hope.
Messi clinched the game with a run and finish before assisting late strikes from Gerard Pique and Ousmane Dembele.
Barcelona will discover their quarter-final and potential semi-final opponents on Friday at 11:00 GMT.
Manchester City, Manchester United, Liverpool, Tottenham Hotspur, Juventus, Ajax and Porto are their potential rivals,