After going in goalless at half-time, Greenwood opened the scoring with a cool, left-footed finish, courtesy of Fernandes’ smart dummy inside the area.
Chris Wood got their first and Henderson was very relieved to discover that the Burnley striker was offside when he headed the ball into an empty net.
Henderson did not inspire a great deal of confidence, it has to be said.
Early in the second half, just 116 second after he had conceded an equaliser to James Tarkowski and now wearing a distinctive red cap to block out the sun, he came out to claim another long ball forward from Lowton and this time got nowhere near it, instead clattering into Victor Lindelof.
It was the 1,000th goal United have conceded in the Premier League.
Many will recall that they also conceded the first of the then new competition in 1992 to Sheffield United’s Brian Deane, a memory that carries even greater resonance as they attempt to break away.
Greenwood restored United’s lead with a deflected finish in the 84th minute.
The Clarets sent numbers forward in search of an equaliser, which allowed van de Beek to tee up Cavani on the counter-attack to seal a 3-1 victory in additional time.
The local rivalry. The history. Because if Manchester United and their friends from the proposed new European Super League have their way, it will soon be a thing of the past.
Burnley, lest we forget, were one of the 12 founder members of the original Football League in 1888. Four years later they played Newton Heath in September 1892, the first of 132 meetings between these two clubs.
Yet United, Chelsea, Arsenal, Liverpool, Tottenham, Manchester City and their European cohorts have their sights on bigger and better things; a new competition that would make fixtures between United and Burnley impossible by as early as next year.
The last time Burnley left Old Trafford after a 2-0 win here last season, there was mutiny in the air and fury from supporters towards the club’s American owners and executive vice-chairman Ed Woodward.
Some will be equally angry now at the greed of the Americans. Others will no doubt be more philosophical.
The notion of a breakaway league has always had the capacity to split opinion in football.
United’s victory here means they have won 64 times to Burnley’s 45, hardly a landslide.
In fact, Sean Dyche’s side could have become only the second club to avoid defeat in five successive Premier League games at Old Trafford after Chelsea in 1998.
The Red Devils, who have now won five top-flight games on the bounce, travel to rivals Leeds United next Sunday before their Europa League semi-final clash with Roma the following Thursday.
The Clarets, who are six points clear of 18th-placed Fulham, visit Wolves next as they look to end their poor run of form.