The Brazilian striker, reportedly pondering a 222-million euro ($256.8 million) move to Paris Saint-Germain, showed why the French club would be willing to pay a world-record price to get him.
He delivered his third goal in two matches in the exhibition tournament as Barcelona handed the English Premiership club their first defeat of the pre-season.
After a bright start Manchester United struggled to contain Barcelona's star duo of Neymar and Lionel Messi. Neymar broke through in the 31st, stripping the ball from Antonio Valencia in the penalty area, turning and finding the net.
The goal proved enough to give a second straight victory to new Barcelona coach Ernesto Valverde. Valverde made sweeping changes to the team that beat Juventus 2-1. Luis Suarez, Jordi Alba, Samuel Umtiti, Nelson Semedo, Sergio Busquets and 19-year-old midfielder Carles Arena were included in the lineup headed by Messi and Neymar.
There were eight changes to the Manchester United team that defeated Real Madrid on penalties on Sunday, with captain Michael Carrick, Marcus Rashford and Jesse Lingard the only players to retain their starting spots.
It was Manchester United who threatened first, when Rashford's cross found Romelu Lukaku in the area, but the Belgian couldn't find the net.
Barcelona inexorably took control, and United goalkeeper David de Gea was given plenty of work by Neymar, Messi and Suarez. Messi came close in the 12th minute, his low effort sliding wide.
A long-range effort from Lukaku, a fierce blast from Paul Pogba and a curling effort from Rashford all tested Barcelona keeper Jasper Cillessen in the space of minutes.
But from there Barcelona dominated. De Gea denied Neymar from close range in the 28th, but had no answer for the Brazilian three minutes later. Valencia had got control of a pass from Messi, but Neymar was there to regain the ball, turning in close quarters and firing past de Gea to the delight of the Barcelona fans among the 82,000-strong crowd at FedExField -- home of the NFL's Washington Redskins.
Three minutes before the break de Gea parried Suarez's scissor-kick to keep it 1-0 to Barcelona at halftime. Both coaches rang the changes at halftime, with Valverde replacing 10 players -- only leaving Cillessen in goal. Jose Mourinho made five changes in his Manchester United side, and the second half moved at a slower, less fluent pace. Anthony Martial, Andreas Pereira and Pogba all threatened, but Manchester United were unable to find an equaliser.