The Chile international, who completed a transfer from Arsenal in a straight swap with Henrikh Mkhitaryan in January, made his debut against Yeovil Town in the FA Cup last week, picking up an assist in the contest.
While he enjoyed a fine debut, Sanchez failed to make an impact on his Premier League bow for United in a disappointing midweek 2-0 defeat to Tottenham.
With the Red Devils in search of points in an ever-tightening top-four race, Sanchez received a golden opportunity to get his first United goal against the Terriers when he was brought down in the area by Michael Hefele to earn the spot-kick.
Sanchez's effort was tame as he put a low shot just to the right of Jonas Lossl, but the Huddersfield goalkeeper could only push it away, right back into the path of the forward, who buried rebound to give the Red Devils a 2-0 advantage in the 68th minute.
Romelu Lukaku had broken the deadlock at Old Trafford in the 55th minute and United comfortably saw out the closing stages for the 2-0 win.
While it was the first goal for Sanchez with United, it was his eighth of the Premier League season to go along with three assists. He remains far off the pace he set last season, when he scored 24 times for the Gunners, while adding 10 assists, in 38 league appearances.
It hasn't quite been a perfect game for Sanchez as he has at times struggled to keep possession, losing it more often on Saturday than any other Red Devils player has all season.
32 - Alexis Sanchez has lost possession of the ball more often today than any Manchester United player has in any Premier League game this season. Loose.— OptaJoe (@OptaJoe) February 3, 2018
But, with the penalty won and the goal scored, Jose Mourinho is more likely to forgive his new attacker as the Red Devils earned three points in their fight for a guaranteed place in next year's Champions League.