Manchester United claimed victory in the first ever Manchester derby to be held overseas.
City, playing their first game of the summer, had a couple of sights of goal in the first half as David de Gea saved well from Raheem Sterling and home-grown youngster Phil Foden.
A heroic double tackle and block from Chris Smalling, as if he knew he was playing his United future, also kept the score at 0-0 at the half hour mark. But United then scored twice in quick succession towards the end of the half to kill the game as a contest.
It was Lukaku who broke the deadlock. The Belgian's second pre-season goal for the club came as he beat new City goalkeeper Ederson to a long pass from Paul Pogba, rounding the £34m Brazilian and firing home from a difficult angle first time - a sign of a player high on confidence.
That lead was doubled moments later when Henrikh Mkhitaryan, a player currently in outstanding form, split the City defence with a driving run and fed Rashford to net his third of the summer.
The teenager almost caught Ederson out with a speculatively effort from range after the break - the City goalkeeper has a way to go to justify his price tag - while Lukaku later cracked a drive against the angle of post and crossbar that threatened to shatter the frame of the goal.
Speaking to MUTV afterwards, Pogba expressed his delight at seeing United's strikers in such good form this early in the campaign.
"Last season we missed a lot of chances and we need to score goals," he said.
"When we have chances we need to kill. A 1-0 win and three points are very important in the Premier League and we know that. So now we have to start scoring goals. We have done it today and we have to keep this mentality."
United now face further tour games against Real Madrid and Barcelona in the coming five days.