Romelu Lukaku opened the scoring in the second half before Sanchez got on the board, missing a penalty but converting the rebound.
Here's the team sheet, via the Times' Paul Hirst:
Old Trafford observed a minute of silence before kick-off to commemorate the Munich air disaster, which happened 60 years ago.
Huddersfield started the match with a tight defensive formation, but a probing United squad got looks on goal early. Jesse Lingard forced a save by stopper Jonas Lossl after a good run and a solid shot, and Chris Smalling aimed a header at the goalkeeper.
The visitors did not shy away from physical play, leading to several incidents in the first half. Scott McTominay got taken out by Terence Kongolo, and to the surprise of many, the official didn't even award a foul.
Sports writer Jonas Giaever couldn't believe it:
Minutes later, Philip Billing was booked for another poor tackle, this one on Marcos Rojo.
Lossl made a fine save to deny Sanchez, who wanted a penalty after a tussle with Kongolo just before the half-hour mark.
Lingard couldn't lift the ball past Lossl, who stayed on his feet long enough, and his shot minutes later didn't beat the goalkeeper, either.
The Terriers did a fine job of frustrating the hosts, and just before half-time, January addition Sanchez was booked, bringing an end to a poor half for the Chilean. Sports writer Nick Miller was not impressed:
The Red Devils came out with more intensity to start the second half, and Sanchez and Lingard had good looks on goal early, with the latter firing over.
Huddersfield were reeling, and after 55 minutes, Lukaku finally found the breakthrough. Juan Mata made the perfect delivery, and the Belgian timed his run well before placing his volley.
The Manchester Evening News' Samuel Luckhurst loved it:
United continued to dominate, and manager Jose Mourinho introduced Paul Pogba after 65 minutes to turn the screws even more.
Just a few minutes later, Sanchez was brought down inside the penalty box, and the former Arsenal man scored his debut goal after Lossl saved his spot-kick.
Pogba and Lukaku went close to adding a third goal but missed the target before United dropped the pace and shut the Terriers attack down.
United's next outing will be against Newcastle, while Huddersfield face Birmingham in an FA Cup replay.