Marcus Rashford scored an early first-half brace to set the Red Devils on their way before Marouane Fellaini added a third to give Jose Mourinho's side complete control of the match at the halfway stage.
A new XI took to the field for the second half and goals from Henrikh Mkhitaryan and Anthony Martial underlined United's dominance before a late brace from Giovani dos Santos made the score look more respectable for the hosts.
New United signings Victor Lindelof and Romelu Lukaku were forced to wait for their debuts having been left out of the starting XI, but Rashford fired an early message to the latter that he faces a battle for the main striking role at the club when he opened the scoring after less than two minutes.
Galaxy full-back Nathan Smith was caught in possession by Jesse Lingard, who poked the ball through for Rashford to curl his finish into the bottom corner with aplomb and get United's 2017-18 campaign off to a perfect start.
The England international came close again 10 minutes later when he cut inside from the right flank before firing an effort wide of the target with the outside of his boot as United continued to dominate their American hosts.
It took a scrambling save from Jon Kempin to deny Juan Mata a sublime second moments later when the Spaniard attempted an audacious lob from the edge of the area, almost catching the Galaxy goalkeeper off guard.
United's second goal did arrive after 20 minutes, and again it came as they won possession back inside the Galaxy half, with Ander Herrera stealing the ball before giving it to Mata. Mata in turn played a pass through for Rashford, who again applied a cool finish to double his personal tally.
It took just six minutes for the visitors to add a third too, with Lingard reaching the byline before cutting back and laying the ball off for Fellaini, who swept his finish past the keeper from the edge of the area.
The 3-0 scoreline reflected United's dominance in the opening half-hour, and they almost scored a fourth shortly after Fellaini's strike when Lingard's curling shot landed on the roof of the net.
Rashford then fired another effort over the crossbar before turning provider for Mata, who also missed the target from inside the area when he drilled his strike wide.
United did have the ball in the back of the net for a fourth time moments later when Chris Smalling tucked home a rebound after Kempin had denied new club captain Michael Carrick, but the linesman's flag cut his celebrations short.
Rashford should have completed his first-half hat-trick two minutes before the interval when he beat the offside trap to race clean through on goal, but the youngster was denied by Kempin when he only had the keeper to beat.
Wholesale changes at half time saw Lindelof and Lukaku both introduced for their debuts, and the latter should have marked the occasion by opening his United account inside three minutes when he was teed up by Paul Pogba, only to be denied by replacement Galaxy keeper Brian Rowe.
Martial was the next to come close shortly before the hour mark when he let fly from 30 yards, sending a powerful strike whistling narrowly over the crossbar.
Mkhitaryan burst into life with a rampaging run down the middle before seeing his effort deflect wide moments later, and from a corner shortly afterwards Lindelof also missed the chance to mark his debut with a goal when he got under his shot and ballooned it over the bar.
United's second-half XI did finally add to the scoring with just over 20 minutes remaining when Mkhitaryan latched on to Martial's pass before sending Rowe the wrong way with a smart finish from the edge of the area.
Martial got his own name on the scoresheet five minutes later as United further drove home their dominance, with the French winger applying the finishing touch to Timothy Fosu-Mensah's cut-back.
Martial brought another save from Rowe as he went in search of a second, but it was LA Galaxy who ended the match on top and they pulled their first consolation goal back with just over 10 minutes remaining when Dos Santos combined with Romain Alessandrini before curling a pinpoint finish into the bottom corner.
There was almost a second in the space of two minutes for the hosts when Ashley Cole stood a cross up into the middle, but Joel Pereira reacted well to keep out Alessandrini's header from point-blank range.
Martial then curled another presentable chance off target before the Galaxy pulled a second goal back with the last meaningful action of the match as Dos Santos unwittingly got the final touch to David Romney's header from a corner, diverting it past Pereira.
United's victory was never in doubt, though, and the Red Devils will now turn their attention to Monday's friendly with Real Salt Lake before taking on Manchester City, Real Madrid and Barcelona in the International Champions Cup.