It was excellent first-half from both sides as Ander Herrera, Sergio Agüero and Raheem Sterling having some decent opportunities early on, but The Red Devils stepped up a gear towards the break as Lukaku and Rashford scored two minutes apart.
United took over in the second period with excellent chances for Rashford, Lukaku and Paul Pogba all coming close to a third, Ederson shone with his triple save from Phil Jones but it wasn't enough as the Red Devils controlled the first overseas Manchester derby.
Hit the ground running
Houston was the host for this historic derby and though it was billed as a friendly José Mourinho will want to get one over old rival Pep Guardiola, and it was end-to-end from both sides early on at the NRG Stadium.
Herrera tested the waters early on in the fourth minute, as the Spaniard tried one from distance and new signing Ederson did well to tip it over the crossbar.
City had their first chance four minutes later as Sterling and Agüero combined well, the Argentine did well to cut in and hit a dipping effort but it was straight into the arms of David De Gea.
Sterling decided to have a go himself in the 26th minute as he decided to let one rip from outside the area, it was a stinging effort from the winger but De Gea did well to tip it over the crossbar.
Chris Smalling was called upon just after the half hour mark, his defending was questionable as he pulled the shirt off Patrick Roberts but dived in to block his effort and was up again to block Agüero's follow-up.
In quick succession
The Red Devils looked the side more likely to score as the half was coming to a close, and they ended the game in the space of two minutes as they notched both goals.
Ederson didn't cover himself in glory for the first goal as he came flying off his line to try and confront Lukaku who got on the end of a long ball, the Belgian headed it beyond the Brazilian but the angle was against him but he did brilliantly to find the far corner.
Rashford added a second moments later as they caught the distorted City defence off guard, Henrikh Mkhitaryan ran at the defence before playing it through to running Rashford and he stuck it in the far corner.
Closing in on a third
United didn't let up as the second half got underway, and it must be frustrating to see for the United fans inside the NRG Stadium as The Red Devils couldn't find a third and it wasn't through a lack of trying.
Rashford had a speculative effort in the 52nd minute as he looked to try and find Lukaku running into the middle, however the cross looks to be going over the head of Ederson but he did well to claw it away.
John Stones displayed some comical defending a minute later as he hit chest the ball straight into the feet of Lukaku, the Belgian curled an excellent effort but that clattered the crossbar.
Pogba had a effort of his own in the 65th minute as he wriggles his way into the area, his effort has some of the fans celebrating but it could only find the side netting.
It hadn't been a stellar debut for Ederson but he showed something for City fans to get excited about in the 77th minute, a corner in was knocked down by Marouane Fellaini into the feet of Jones and the Brazilian pulled an excellent triple save to deny him and Lukaku's resulting effort was flagged offside.