Jose Mourinho’s side emerged victorious in the first Manchester derby to be held outside of the UK.
Mourinho got the better of his arch managerial rival Pep Guardiola, whose City side looked understandably rusty in their first pre-season encounter.
Lukaku’s second goal of the tour since his £75million move from Everton was an outrageous strike, the forward converting from way out from the tightest of angles.
United’s second came a minute later, Rashford seizing on sloppy defending from City to drill his shot past Edersen, who had a debut to forget for the Blues.
Here are five things we learned from the Houston encounter:
1. City’s goalkeeping woes continue
Claudio Bravo was supposed to be an upgrade on Joe Hart, but that decision backfired on Pep Guardiola last season. Ederson, a £35million arrival from Benfica, was supposed to be an upgrade on Bravo, but his error-strewn debut here suggested otherwise.
He came racing off his line to win the ball but was beaten to it by Romelu Lukaku, who scored from an outrageous angle, and conceded a minute later when Marcus Rashford beat him with a low angled shot.
Rashford almost caught him out again with a long-range effort after the break, but Edersen managed to tip it away.
2. Lukaku made his outrageous goal look easy
The sign of a great striker is the ability to make difficult finishes look easy, but Lukaku went one better here: he made a seemingly impossible opening look simple.
Having shown great courage and determination to beat Edersen to the ball with his head, Lukaku showed great technique, vision and execution to steer his shot into the net from the tightest of angles, for his second United goal in three games since his £75million move from Everton.
He also hit the bar after the break with a ferocious effort.
3. United’s best central defensive pairing still to be decided
When Jose Mourinho signed Victor Lindelof from Benfica for £30m, it was naturally assumed the Sweden international would partner Eric Bailly to make up United’s first-choice central defensive pairing.
That may still be the case, but with Lindelof finding his feet on tour and not looking entirely convincing so far, the identity of Bailly’s central defensive partner for the season opener at home to West Ham on August 13 is not a given.
Bailly and Jones looked more a convincing pairing in the second-half than Smalling and Lindelof in the first, and Mourinho has a dilemma to address.
4. City’s youngsters impress despite defeat
Guardiola picked a team containing established faces like Sergio Aguero, Yaya Toure, Kevin De Bruyne and Raheem Sterling, but it was two of City’s youngsters, Stockport-born Phil Foden and Patrick Roberts, who made the biggest impression.
Foden impressed with his touch, movement, quick feer and clever use of the ball, while Roberts, who has returned from a loan spell at Celtic, tormented Daley Blind, the United player resorting to crude tactics to stop him and earning a yellow card in the process.
5. Aguero a no-show in first-half outing
On the day it emerged City are one of the clubs that have angered Monaco with an alleged illegal approach to their £100m-rated young forward Kylian Mbappe, their star striker Sergio Aguero did little to convince his employers they do not need to sign the precociously-talented 18-year-old.
Aguero did nothing of note in his 45-minute outing, and it remains to be seen what impact City’s pursuit of Mbappe – if successful – will have on Aguero, whose future remains uncertain, particularly with Gabriel Jesus fully fit again and City in the race for Mbappe.