United boss Ole Gunnar Solskjaer made four changes to the side beaten 1-0 at Bournemouth last time out, with Sergio Romero, Marcos Rojo, Juan Mata and Mason Greenwood starting in place of David de Gea, Victor Lindelof, Daniel James and Andreas Pereira.
The Red Devils edged a 1-0 victory in Belgrade two weeks ago, with Anthony Martial scoring from the penalty spot just before half-time.
Both sides saw early efforts chalked off for offside, before England striker Marcus Rashford twice failed to convert when he should have done better.
With just over 20 minutes played United hit the front as Rashford found Greenwood, who brought the ball back on to his favoured left foot and finished confidently past Vladimir Stojkovic.
Ten minutes later it was 2-0 thanks to a fine individual effort from French striker Anthony Martial, who skipped away from a couple of defenders before poking a neat finish past the advancing Stojkovic.
Early in the second half the hosts put the game to bed with a third goal, as Ashley Young fed Rashford and this time he made no mistake by rifling a left-foot shot past the stranded Stojkovic.
Soon after Stojkovic denied Rashford as the home side went in search of further goals, although they did suffer a blow 15 minutes from time when midfielder Scott McTominay was forced off due to a leg injury.