The Belgium striker showed skill, strength and balance to put Jose Mourinho's men ahead inside three minutes, then raced through to put the tie out of sight in the 55th minute.
However, the game wasn't without controversy as the tested Video Assistant Referee (VAR) technology was utilised to rule out a Juan Mata effort on the stroke of half-time.
Have a look at Blake Welton's quick-fire highlights from this evening's John Smith's Stadium clash
2 Minutes: Collin Quaner drives into the box before seeing his low effort go wide.
10 Minutes: Another van La Parra corner bounces before falling to Billing who’s stinging half-volley fires off Victor Lindelöf.
14 Minutes: Florent Hadergjonaj cuts in from the right and drills a low effort straight into the hands of Sergio Romero.
18 Minutes: Schindler blocks an initial Chris Smalling effort from a corner before beating him in the area again when the ball comes back in.
22 Minutes: Danny Williams drives into the area and clips a cross towards the penalty spot; the ball is met by the head of van La Parra but it’s a comfortable save for Romero.
23 Minutes: Hadergjonaj whips a dangerous ball into the area but Ince can’t get a good enough contact on it.
28 Minutes: Williams tries his luck from range but the 30 yard effort was never going to test Romero.
33 Minutes: Billing tries a curling effort from 30 yards out which is dealt with well by Romero.
45 Minutes: Juan Mata has the ball in the net after a smart Manchester United counter-attack but it's disallowed after consulting VAR.
52 Minutes: Appeals for a penalty as Schindler goes down in the box after an aerial challenge but the referee says no.
55 Minutes: GOAL! Lukaku doubles United’s lead - Alexis Sanchez finds his strike partner after a quick break and he coolly slots home.
72 Minutes: Schindler does well to block Lukaku - the ball was cut back to the forward with the defender getting his body in the way.
74 Minutes: Billing collects the ball 20 yards out and drives into the area before seeing his effort saved by Romero.
85 Minutes: An Ince corner is met by an unmarked Abdelhamid Sabiri five yards out but he couldn’t keep his header down.
86 Minutes: Billing and Mounie link-up well before the former tries to slip Scott Malone into the area but United keeper Romero was alert to it.
89 Minutes: A Williams’ cross picks out Mounie 10 yards out but the striker’s acrobatic effort is just wide.
Huddersfield Town (4-2-3-1): Lossl, Hadergjonaj (Smith, 70), Schindler, Zanka, Kongolo (Malone, 70); Billing, Williams; Van La Parra (Sabiri, 84), Ince, Quaner; Mounie.
Subs Not Used: Coleman, Whitehead, Hogg, Depoitre.
Manchester United (4-2-3-1): Romero; Young, Lindelof, Smalling, Shaw; Matic, Carrick; McTominay, Mata (Lingard, 80), Sanchez (Martial, 76); Lukaku (Bailly (90+1).
Subs Not Used: Periera, Darmian, Gomes, Hamilton.
Half time: Huddersfield Town 0 Manchester United 1
Next match: West Bromwich Albion at the Hawthorns, Premier League, Saturday, February 24 (kick off 3pm)