United dominated possession throughout against the relegation-threatened visitors, but it took until the 55th minute for them to find the breakthrough courtesy of a Romelu Lukaku strike.
Sanchez then added a second on a comfortable afternoon for the home side, tucking home a rebound after seeing his initial penalty saved by Huddersfield keeper Jonas Lossl.
The win sees United increase the gap to fifth-placed Tottenham Hotspur back to eight points, whereas Huddersfield drop into the relegation zone following a fifth successive Premier League defeat.
United boss Jose Mourinho reacted to Wednesday's 2-0 defeat at the hands of Tottenham Hotspur by dropping the likes of Paul Pogba, Ashley Young and Phil Jones from his starting lineup, handing surprise starts to Luke Shaw, Scott McTominay and Marcos Rojo.
January arrival Sanchez did make his Old Trafford bow for the club, although even with their new number seven United struggled to break down Huddersfield despite dominating possession in the first half.
The hosts' first chance of the contest arrived after only eight minutes as Jesse Lingard burst through the middle of the park before drilling a powerful low strike towards goal which Lossl got down well to save.
Chris Smalling drew a routine stop from the Huddersfield keeper moments later, but the biggest talking point of the first half arrived in the 19th minute when McTominay was flattened inside the area by Terence Kongolo.
The Huddersfield defender was late with an aerial challenge and left McTominay in a heap on the floor, but referee Stuart Attwell decided against awarding the hosts a penalty.
It was a quiet start to the match from Sanchez, but the Chilean burst into life shortly before the half-hour mark when he cut inside before letting fly from just outside the area, forcing Lossl into a smart save to his right.
Lossl was by far the busier of the two keepers throughout, and he was called into action again to deny Lingard twice more before half time as United continued to toil for a way through.
The hosts made a quicker start to the second half, though, with Sanchez being thwarted by blocks from Tommy Smith and Kongolo before Lingard also skewed a wild effort off target from the edge of the area.
The breakthrough finally arrived 10 minutes into the second half when Lukaku got in front of his marker to meet a Juan Mata cross from the left, steering a well-controlled volley past Lossl at the near post.
The same pair linked up again shortly after the hour mark only for Lukaku to this time send a header well off target, but the hosts did have their second goal shortly afterwards as Sanchez scored his first goal for the club.
The Chilean was brought down inside the area by a mistimed Michael Hefele challenge but saw his resulting spot kick saved, only to tuck home the rebound after the ball fell straight back to him.
Pogba, who was brought off the bench for the final 25 minutes, then fired an effort well off target from range, but the closing stages were quiet as United comfortably saw out the game with no danger of Huddersfield clawing their way back into it.
The Terriers failed to have a single shot on target throughout the match as they suffered a fifth straight defeat with a whimper, leaving them in the relegation zone and still pointless so far in 2018.
David Wagner's side are also winless in their last eight league games and have now won just once in their last 12 on the road, failing to back up their famous victory in the reverse fixture following a tepid display at Old Trafford.
United, meanwhile, remain second and close the gap on leaders Manchester City to 13 points having swiftly returned to winning ways following their slip-up against Spurs in midweek.
MAN UTD (4-2-3-1): De Gea; Valencia, Smalling, Rojo, Shaw; McTominay, Matic, Mata (Rashford, 71'), Lingard (Pogba, 65'), Sanchez; Lukaku (Martial, 77')
HUDDERSFIELD (4-5-1): Lossl; Smith, Zanka, Schindler (Hefele, 59'), Kongolo; Quander, Hadergjonaj, Hogg, Billing (Mooy, 33'), Van la Parra (Ince, 69'); Depoitre body check tags ::