Marouane Fellaini, Henrikh Mkhitaryan and Anthony Martial added the other goals for the visitors, before Galaxy replied with two consolation strikes through Giovani dos Santos and Dave Romney in the closing stages.
Lukaku had a great chance to open his account after receiving a pass from Pogba in the 49th minute, but Brian Rowe - who replaced Kempin - made a good save.
United boss José Mourinho has said it is "possible" Zlatan will be offered a new contract, and the fans have been positively reacting to this development on the club's official social media pages.
It didn't take long for the Reds to get off the mark with Rashford finding the net within just 2 minutes.
Fireworks were followed by ticker tape at the kick-off - paper that was still floating to the ground when Jesse Lingard snatched possession, allowing Rashford to finish smartly after 115 seconds.
Watch the three first-half goals below.
"It's just natural evolution of a kid", said Jose Mourinho after the game.
The Spain worldwide played through the sharp-looking striker, who showed no little composure and skill to slot past Jon Kempin.
On Morata's failed move, the Portuguese said: "I don't like to speak about players who aren't ours, because Morata is not our player". We have players on the pitch with problems. A real positive experience to get us ready for a real dog fight in the second half of the season.
Lukaku, who joined United for a reported £75million from Everton earlier this month, played the second half at StubHub Center in California. Then comes a three-game run in the International Champions Cup, with games against rival Manchester City (July 20) in Houston, Real Madrid (July 23) in Santa Clara and FC Barcelona, July 26 in Maryland.
Mourinho has plenty of options with his squad and will hope to continue rotating players and try to find his best tactics before the new Premier League season. The pace when he builds up a head of steam instantly turns defence into attack and may cure United of some of the stodgy approach play which hampered them too frequently last season.