Wayne Rooney scored twice before the interval in Denver, his second coming from the penalty spot, with Juan Mata on target in between with a deft finish from the England international’s superb pass.
Substitute Miralem Pjanic pulled one back for Roma with an astonishing long-range goal from well inside his own half in the 76th minute, leaving second-half goalkeeper Ben Amos red-faced, before Francesco Totti's late penalty left United hanging on somewhat ahead of further meetings with Inter Milan and Real Madrid.
Louis van Gaal's men had brushed aside LA Galaxy 7-0 earlier in the week and followed up that romp with a further three goals against the Serie A side, in a game where midfielder Tom Cleverley was handed the captain's armband.
There were some nervous moments for the Premier League club in the opening exchanges, with Roma striker Mattia Destro twice going close to opening the scoring.
Destro's first attempt came with just two minutes on the clock when he got in behind United's three-man defence and lifted the ball over goalkeeper Sam Johnstone, only to see it somehow bounce over the bar from barely two yards out off the firm Sports Authority Field surface.
And he will feel he should have done better soon after when the ball broke to him following Salih Ucan's run, but he could only side-foot over the crossbar from the edge of the area.
It took United some time to get into their stride in the heat and altitude, with Danny Welbeck charging down Lukasz Skorupski's attempted clearance before his attempted pull-back to Mata was cleared away.
A previously lacklustre game then exploded into life in the final nine minutes of the half, with Rooney breaking the deadlock with a stunning finish from outside the box which arced over the helpless Skorupski and into the top corner.
Rooney then turned provider, lifting a sublime pass from inside his own half into the feet of Mata, who controlled the ball with his first touch and then lifted a clever chip over the on-rushing keeper with his second.
And it was 3-0 before the interval as Welbeck was felled by Urby Emanuelson followed Ander Herrera's pass, with Rooney stepping up to send Skorupski the wrong way as he slammed the penalty home.
Van Gaal made a host of changes at the interval, with only Cleverley and young defender Tyler Blackett left on from the starting XI, while Roma counterpart Rudi Garcia also tinkered with his side as the familiar face of former Chelsea left-back Ashley Cole joined the fray.
Destro looked a threat again early in the second half as he dribbled his way into space in the United box before attempting an overly ambitious shot from a very tight angle which flew beyond Amos and into the side-netting.
Will Keane saw his penalty appeals waved away and was ruled to have fouled Mehdi Benatia as they battled for the ball in the Roma box, before Alessandro Florenzi fired a first-time effort from inside the area wide of Amos' goal.
The flow of the game, which had been disrupted by the interval changes, was further affected by another raft of Roma substitutions midway through the second period, which included the introduction of the iconic Totti.
Cleverley, who did little to impress in his outing as captain, was replaced by Javier Hernandez soon after, with Chris Smalling the man to take over as United's skipper for the remainder of the game.
Pjanic scored the goal of the match with 14 minutes remaining as he received possession inside his own half, looked up to spot Amos off his line before launching an audacious attempt which flew over the frantically back-tracking keeper and under the crossbar.
Amos redeemed himself to an extent with six minutes remaining as he got his fingertips to an overhead kick from Leandro Castan from only eight yards out onto the inside of his post before the ball was cleared to safety.
Referee Alan Chapman pointed to the spot in the closing moments after Michael Keane was ruled to have handled in the box, allowing Totti to step up and beat Amos from 12 yards out.