United got off the perfect start by taking the lead after two minutes as Romelu Lukaku out-muscled his marker before firing home from close range.
The hosts were deterred by conceding as they controlled a lot of the ball and managed to carve out a couple chances in the opening 20 minutes.
The Red Devils thought they had doubled their lead just before the break but Juan Mata's goal was ruled offside by the Video Assitant Referee (VAR).
Nevertheless, Jose Mourinho's charges went into the break with a one-goal advantage.
10 minutes into the second half, United got their second goal as Lukaku latched onto a fine pass from Sanchez before slotting home from close range.
Huddersfield made a double switch on 70 minutes, bringing on Tommy Smith and Scott Malone.
Mourinho made a couple changes of his own with 15 minutes remaining as Anthony Martial and Jesse Lingard replaced Sanchez and Mata.
The hosts continued to push for a first goal in the closing stages but United held on to claim the 2-0 win.