The striker scored in each half to secure the win, although there was more Video Assistant Referee (VAR) controversy when Juan Mata saw a goal disallowed for offside.
Jose Mourinho made six changes to his side, with Sergio Romero taking over in goal from David De Gea, while Victor Lindelof and Scott McTominay also started. Simon Peach at the Press Association shared the two teams:
The visitors opened the scoring after just three minutes. Mata sent Lukaku racing through on goal, and he checked back before firing a low shot past goalkeeper Jonas Lossl.
The goal means the striker maintained his record of scoring in every round of the competition for United this season:
Huddersfield responded well to going behind and forced United back, but they struggled to work Romero. The visitors, meanwhile, looked disorganised, and it was difficult to comprehend their game plan, according to football writer Liam Canning:
However, the Red Devils thought they had doubled their lead just before half-time when Ashley Young found Mata, who rounded Lossl and slotted home.
United celebrated the goal, but referee Kevin Friend opted to refer the decision to the VAR, who ruled it offside. ESPN FC's Alex Shaw neatly summed up the process:
Football commentator Arlo White gave another view of the goal:
Mourinho's side then had another goal disallowed after Nemanja Matic stroked home Alexis Sanchez's free-kick from an offside position, but this time the decision was a lot easier for the officials.
Huddersfield continued to look the better side after the break but slipped 2-0 down after being caught on the counter. Sanchez fed Lukaku, who raced through and finished clinically despite the attention of Danny Williams.
ESPN FC's Rob Dawson showed how clinical the visitors had been:
The second goal seemed to drain the belief out of Huddersfield, and even though they enjoyed plenty of possession, United comfortably held them at bay.
It was a welcome victory for the Red Devils after their 1-0 defeat to Newcastle United last time out, and their hopes of ending the season with some domestic silverware were maintained.