A defeat for United would have seen it suffer three losses in its opening five Premier League games for the first time, but it picked up where it left off against Burnley prior to the international break, professionally dealing with an in-form Watford side.
Although the hosts initially looked bright, United finished the first half utterly dominant and 2-0 up thanks to Romelu Lukaku and Chris Smalling, whose goals were three minutes and 11 seconds apart.
Watford at least made things interesting with a 65th-minute Andre Gray strike, but United dug deep and fended off the home side's late advances to seal the points, despite Nemanja Matic's red card deep into stoppage-time.
Confidence appeared to be flowing through Watford early on and they went close to the opener through Troy Deeney, but David de Gea was United's saviour, tipping the striker's effort over.
United did manage to settle, however, and ultimately capitalised on De Gea's heroics with two quick-fire goals late in the half.
Lukaku bundled in the first when latching on to Ashley Young's deflected cross 10 minutes from the break, before Marouane Fellaini headed a corner back into the danger zone and Smalling smashed home.
United was not quite so dominant after the restart and Watford found a foothold which ultimately allowed it to reduce the arrears, Gray finding the top-right corner from Abdoulaye Doucoure's cut-back.
Unfortunately for Watford, that goal was not the start of a turnaround, and United clung on to a second consecutive victory after Matic received a second caution, De Gea denying Christian Kabasele from the resulting free-kick.
A hectic week is ahead for United, which begins its UEFA Champions League campaign at Young Boys on Thursday (AEST), before returning to Premier League action at home to Wolverhampton Wanderers.
Watford, on the other hand, travels to Fulham next weekend.