Real went into the match brimming with confidence from a run of six wins and one draw in its last seven matches, but were given a run for their money by a spirited Ajax team.
The teenager became the youngest Italian player to score two goals in a Champions League match as he led Roma to a 2-1 win at home against Porto in the first leg of the round of 16.
Old Trafford instead became a stage for Kylian Mbappe to shine in tandem with Angel Di Maria, who relished the revenge mission on his return to his former club.
The knockout stages begin Tuesday with Manchester United hosting Paris Saint-Germain and Porto going to Roma in the first leg of the round of 16 games.
PSG will be without the world's most expensive player Neymar and possibly 192-goal, all-time club leading scorer Edinson Cavani against a revitalized United side unbeaten under their new coach Ole Gunnar Solskjaer.
PSG will travel to Manchester for the first leg of the Champions League round of 16 clash on February 12.
All four of England's representatives have advanced for the second straight season, even if two of them — Liverpool and Tottenham — left it to their final matches.
Dortmund finished level on points with Atletico in Group A and sealed top spot thanks to a better goal difference.
It was Mohamed Salah's latest wonder-goal — an individual effort scored in the 34th minute — that was the difference between the teams on another atmospheric European night at Anfield.
Cavani and Neymar were both assisted by their 19-year-old teammate, with Mbappe putting on an excellent display of speed, strength and dribbling throughout the game.
Mauricio Pochettino's team will now look to improve on their round-of-16 exit last season when they lost to Juventus 4-3 on aggregate.
Jose Mourinho picked up a basket of water bottles and threw them to the ground after Marouane Fellaini scored in stoppage time to earn Manchester United a 1-0 win over Young Boys.
Paris Saint-Germain will play Liverpool on Wednesday in their Champions League fixture at the Parc des Princes.
Milan Pavkov scored in the 22nd and 29th minutes as the Serbian champions earned a first win in their debut appearance in the Champions League group stage.
Barcelona visit Inter Milan with hope that Lionel Messi can return after recovering from a broken arm.
The defeat against Juventus leaves United with just one win from its last seven games as Mourinho's men struggle to make much headway on the roads or on the field.
The Portuguese coach appears to have recovered confidence after a 3-2 home win against Newcastle and a 2-2 draw away to Chelsea.
The football superstar has been accused of rape in the United States. Kathryn Mayorga filed a civil lawsuit last month in Nevada claiming Ronaldo raped her in his Las Vegas hotel room.
Messi will miss playing Inter Milan in the Champions League on Wednesday, and El Clasico against Real Madrid next weekend.
Barcelona won the Champions League title at Wembley in 2011, beating Manchester United 3-1.
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