A year after the first attempt at an overseas derby in China was cancelled, the two sides finally met in the International Champions Cup match in Houston, Texas, on Thursday night and it was Jose Mourinho's side who took the bragging rights.
Lukaku scored his second pre-season goal in the 37th minute as he rounded new Man City goalkeeper Ederson before slotting into an open net in front of a crowd of 67,401 at the home of NFL's Houston Texans.
Two minutes later and Rashford - who has been touted by Mourinho as a strike partner for Lukaku - doubled United's lead as he hit home on a tight angle to seal the victory.
Man Utd made a fast start at the NRG Stadium, and Ederson looked to be in fine form on his City debut with the goalkeeper making three fantastic saves in the first 25 minutes. Kyle Walker was also playing in a City shirt on for the first time.
Ederson twice kept out long-range efforts, first from Ander Herrera and then from Henrikh Mkhitaryan's half volley, with David de Gea also in action at the other end as he acrobatically tipped a Raheem Sterling effort over the crossbar.
United finally took advantage of their first-half chances as Lukaku netted in the 37th minute. Paul Pogba played a sumptuous long pass up the field, picking out the run of the striker, who took the ball around the oncoming Ederson before slotting home in front of Vincent Kompany and Tosin Adarabioyo.
Rashford also got in on the scoring action with his third goal in three pre-season games in the 39th minute. Mkhitaryan laid the ball off to the young forward on the right side of the box, allowing him to sweep home from an angle to put United further ahead.
After changes from both sides at half-time, it was United who continued to see the better of the chances. Lukaku could have added a second to his personal tally nine minutes after the restart, but his thunderbolt effort hammered against the top corner of the crossbar.
With an assist to his name, Pogba could also have nabbed a goal in the 65th minute as his curling shot looked to be heading past Ederson but it could only graze the side of the net.
The City stopper did well to deny United a third goal with 11 minutes of the game to play, stopping Phil Jones at point-blank range three times in quick succession and while Lukaku netted the rebound, he was flagged for offside.
City attempted to rally in the final few minutes as Samir Nasri's cross just evaded the foot of Gabriel Jesus before Fernandinho forced second-half goalkeeper Sergio Romero into a fingertip save, but United held out for the victory.
Man of the match - Romelu Lukaku
Another pre-season match and another impressive display from the big Belgian, who netted in his second successive game and could arguably have bagged another couple of goals.
He never stopped working in attack for United - pointing at the badge after his goal - and was a menace to the City back-line when he got into full flow, which should be a concern for the upcoming Premier League defences.
His budding strike partnership with Rashford looks to be an exciting prospect and if the two can keep working on their game together, they could be a potent force next season.
