Watford have never won at Old Trafford in the league and once playmaker Mata swept in after 32 minutes that sorry statistic was in no danger.
"In the first half the football was fabulous. The fans got behind the team just before we scored the goal because we were phenomenal," United manager Jose Mourinho told the BBC.
The hosts attacked in waves early on and only great saves by Watford keeper Heurelho Gomes from Paul Pogba and Zlatan Ibrahimovic kept them out.
United deservedly scored when Martial was set free down the left by Henrikh Mkhitaryan and his pass was met by Mata.
Watford, who arrived on a four-match unbeaten run in the league, offered more after the break and home keeper David de Gea had to claw out Mauro Zarate's curling free kick.
United still dominated though and doubled their lead on the hour when Martial was played in by Ibrahimovic's clever touch and he wrong-footed Gomes at the near post for only his third league goal of the season.
"Martial deserves the chance. He has worked harder than ever in the last two weeks in the way I like -- silence but hard," Mourinho said of his French forward.
United are on the longest unbeaten run of any club in Europe's top five domestic leagues and moved above Liverpool into fifth place with 48 points before Liverpool host second-placed Tottenham Hotspur (50) later.
(Reporting by Martyn Herman, editing by Ed Osmond and Toby Davis)
