Fernandes gave United a perfect start in their semi-final with Italian side Roma when he swept home Cavani's first-time lay-off.
Paul Pogba's handball allowed Lorenzo Pellegrini to equalise before the Roma skipper's pass allowed former Manchester City striker Edin Dzeko to score his sixth goal in five Old Trafford appearances to turn the tie on its head by half-time.
But United rallied after the break. Cavani levelled with a superb first-time effort before tapping the hosts back in front when substitute keeper Antonio Mirante pushed Aaron Wan-Bissaka's angled shot into his path.
Ole Gunnar Solskjaer's men were in no mood to let their advantage slip a second time, although it took a fortunate penalty for what seemed to be an innocuous Chris Smalling tackle on Cavani to give Fernandes the chance add a fourth from the spot.
Pogba then powered home a precise header from Fernandes' cross before Greenwood ran on to Cavani's pass and drove home United's sixth, making them the first side to score six goals in a major European semi-final since Real Madrid in the 1964 European Cup.