The Belgian's first came within three minutes and he added a second before the hour mark, after United were made to work by the Terriers at the John Smith's Stadium.
A scorer in the previous two rounds against Derby County and Yeovil Town, Lukaku wasted little time in picking up his good FA Cup form.
Mata himself thought that he had scored in the first half, but his stoppage-time effort was ruled out for offside after referee Kevin Friend referred the decision to VAR.
Huddersfield would have been unfortunate to be two behind at the break having responded well to their early setback to dominate the possession and territory.
Tom Ince squandered the best chance that the Terriers created when he dragged his shot from a tight angle across goal on six minutes, otherwise they were limited to long-range efforts by organised United defending.
After controversially being denied a second by the questionable technology, the Red Devils did double their lead on 55 minutes with Lukaku clinical again.
Sanchez released the 24-year-old with a defence-splitting pass, and he held off Mathias Jorgensen to cooly slot the ball under Lossl on 55 minutes.
By that point, United had withstood Huddersfield's best efforts and they saw out the remainder of the second half without Romero being seriously tested.
Lukaku would have had a hat-trick had Jesse Lingard not misjudged a simple square pass to the Belgian on 83 minutes, but he was the match-winner nonetheless.
United have now reached the last eight of the FA Cup for the fifth time in six seasons while Huddersfield are knocked out in the fifth round for a second straight season.
HUDDERSFIELD (4-4-1-1): Lossl; Hadergjonaj (Smith, 70'), Zanka, Schindler, Kongolo (Malone, 70'); Quaner, Williams, Billing, Van La Parra (Sabiri, 84'); Ince; Mounie
MAN UNITED (4-3-3): Romero; Young, Lindelof, Smalling, Shaw; Matic, Carrick, McTominay; Mata (Lingard, 81'), Alexis (Martial, 75'), Lukaku (Bailly, 90')