Belgian international Lukaku grabbed his second goal in his second start for United as the Red Devils eased past a disjointed City.
Belgian international Lukaku grabbed his second goal in his second start for United as the Red Devils eased past a disjointed City at Houston's NRG Stadium.
England striker Rashford meanwhile continued his impressive pre-season form with his third goal in three games of United's US tour.
The game was the first ever Manchester derby played on foreign soil and both teams commemorated the May 22 attacks at a concert in the city shortly before the kick-off.
"It was a very good training session," United manager Jose Mourinho said afterwards.
"We had to play well in the first half, is good intensity, the players are tired. I am really pleased and I'm sure Pep (Guardiola) is the same. The result is not the most important thing."
City manager Pep Guardiola meanwhile shrugged off the loss, preferring to enthuse about the performance of teenager Phil Foden, a 17-year-old who has emerged from the club's youth set-up.
"I don't have words... It's a long time since I saw a performance like this - it was another level," said Guardiola, who also confirmed that defender Aleksandar Kolarov was on his way out of the club, with Roma the likely destination.
"I don't like working with people who don't want to stay. He has a big chance to go to Roma. He has said he wants to leave," Guardiola said of Kolarov.
Kolarov's looming exit heightens speculation that City are close to signing Monaco fullback Benjamin Mendy.
Earlier, United enjoyed the better of the early exchanges, with Henrikh Mkhitaryan testing new City keeper Ederson with a long-range effort just after 20 minutes.
Ander Herrera also tried his luck from distance shortly afterwards but the young Brazilian gathered comfortably.
At the other end meanwhile, City, who handed a debut to new signing Kyle Walker, slowly got into their stride, with a deflected Raheem Sterling effort tipped over by David De Gea.
City should have had a penalty on 31 minutes when youngster Patrick Roberts was tugged back by Chris Smalling as he burst into the area.
Instead Smalling managed to get a foot in and clear with Sterling's follow-up effort blocked.
Six minutes later United took the lead with a superb goal from Lukaku.
A long clearance from Paul Pogba drew Ederson off his line but Lukaku managed to nod the loose ball past the stranded City goalkeeper before finishing from a tight angle.
Two minutes afterwards, United doubled their lead with another swift counter-attack.
This time it was Mkhitaryan who turned creator, releasing Rashford with a deft pass.
The teenage England striker picked his spot and drilled a low finish across Ederson into the bottom corner.
United continued to enjoy the better chances early in the second half, with Lukaku almost grabbing a second when his curling strike hit the woodwork on 53 minutes.
Both Mourinho and opposite number Guardiola made a flurry of changes throughout the second half as the game fizzled out.