Manchester United will be aiming to overcome a 1-0 deficit at the Nou Camp next week.
Ole Gunnar Solskjaer's side lost narrowly at Old Trafford as Barcelona got a crucial away goal and clean sheet combo.
It took just 12 minutes for Barca to hit the front. Luis Suarez's header at the far post went in off Luke Shaw to make it 1-0.
Man United battled but were unable to find an equaliser as Barcelona maintained their clean sheet.
But United know if they win and score at least twice at the Nou Camp next week, they will advance to the semi-finals.
Easier said than done of course as Barcelona are imperious at the Nou Camp.
Ajax vs Juventus
Meanwhile, Juventus also got an away goal tonight at Ajax. But the Dutch club were able to avoid defeat on home soil.
The returning Cristiano Ronaldo had given Juventus the lead just before half-time with a diving header.
But Ajax were level just after the break. Young Brazilian David Neres, curling in his shot.
They now face a daunting trip to the Juventus Stadium where the Bianconeri rarely taste defeat and where Ajax need to score at least once.