In front of 2,000 home fans, United absolutely dominated proceedings throughout the 90 minutes, but just couldn't find a finish.
Cavani, who netted his first goal for the Reds at Goodison Park in last month's Premier League meeting, stepped up to make the vital breakthrough two minutes from the end, with a brilliant curling effort after being found by substitute Anthony Martial, who himself doubled the margin of victory in the final seconds of injury time.
It was exactly what United deserved and it maintained our superb domestic away form.
FIRST HALF - REDS DOMINATE BUT IT'S DEADLOCK
With three games to come in six days, Ole Gunnar Solskjaer promised changes to his side and he made nine from the XI that started the 6-2 win over Leeds, with Bruno Fernandes and Harry Maguire the only player retained.