Victory over Chelsea on Monday had reinvigorated United's challenge for a top four spot and, while Watford won the reverse fixture in December, they came into this match in 19th place and on a run of four games without a win.
But, despite coming into this match on the back of a positive result, United started the game slugglishly as Watford forward Troy Deeney had the best chance of the opening exchanges.
Yet the home took the lead on 42 minutes after Fernandes was brought down inside the box by goalkeeper Ben Foster. The Portugal international dusted himself down and coolly slotted the ball into the corner.
Watford had the ball in the United net just after half-time after Deeney bundled it home, only for VAR to intervene and the goal was ruled out for a handball by Craig Dawson.
United then added a second on 58 minutes through Martial. The France forward's chance appeared to have gone before a delightful drag-back opened up space and he dinked the ball past Foster.
Greenwood finished emphatically made it 3-0 with 15 minutes remaining as he combined with Fernandes before rifling the ball into the roof of the net.
United move up to fifth -- three points behind fourth-place Chelsea -- while Watford missed the chance to move out of the relegation zone.