The England striker may have endured a frustrating World Cup as his country exited at the group stage but he showcased his talent at club level in front of new United manager Louis van Gaal with a brace - the first a superb distance effort - as the Premier League side enjoyed a good workout in Denver, United States.
Rooney's 36th-minute opener lit up the encounter, the forward hitting an angled finish from 25-yards across Lukasz Skorupski and into the top corner.
His strike was bettered by an even more sensational effort after the break, as Miralem Pjanic lobbed United goalkeeper Ben Amos from well inside his own half, but Van Gaal's side still had enough to open the eight-team pre-season tournament with a win.
After Rooney had netted his first, Juan Mata doubled the English side's advantage, bringing down Rooney's precise ball over the top before lifting a finish over the goalkeeper.
And Roma were the masters of their own downfall just before the break when Danny Welbeck was felled in the box, allowing Rooney to step up and score from the penalty spot.
The Serie A outfit came more into the game in the second period and pulled a goal back with 15 minutes left in spectacular fashion when Pjanic picked the ball up inside his own half and launched a stunning lob over a back-pedalling Amos.
They reduced the deficit further with two minutes left when Michael Keane was adjudged to have handled the ball in the box and Francesco Totti stepped up to score from the penalty spot, but they could not force a draw.
Staying in the USA, Inter came from behind to defeat Real Madrid 3-2 in a penalty shoot-out after the match finished 1-1 through 90 minutes.
Mauro Icardi converted his second penalty of the match to give Inter victory in the International Champions Cup, after his earlier spot-kick had levelled the game, while Walter Mazzarri's Serie A side also had reserve keeper Juan Pablo Carrizo to thank after he made two saves in the shoot-out.
Tottenham completed their tour of the USA undefeated courtesy of a 2-0 win over Chicago Fire, while Aston Villa accounted for Houston Dynamo 1-0.
Meanwhile, in Germany, Wolfsburg will face Bayern Munich in the final of the Telekom Cup on Sunday after winning their respective semi-finals on penalties.
Bundesliga champions Bayern surrendered a two-goal lead against Borussia Monchengladbach before winning the shoot-out 5-4, Julian Korb hitting the crossbar to settle matters.
Robert Lewandowski's stunning chip, allied to Franck Ribery's strike, had put Bayern in command, only for two Max Kruse penalties - the second of which came at the end of normal time - to take the game to spot-kicks.
It finished goalless in normal time between Wolfsburg and Hamburg, with Kerem Demirbay's penalty miss proving pivotal as the shoot-out finished 6-5 to Dieter Hecking's side.
Rio Ferdinand and Bojan Krkic made losing starts with their news clubs as QPR and Stoke City each suffered 2-0 defeats.
Former England defender Ferdinand made his first QPR appearance since arriving as a free agent following his release from Manchester United, but was overshadowed by Bundesliga 2 side RB Leipzig.
A second-half double from Yussuf Poulsen saw the Premier League newcomers deservedly beaten, with Stoke losing by the same margin against another second-tier German side.
Bojan's maiden outing in Stoke colours proved fruitless as the former Barcelona forward was withdrawn at half-time, with 1860 Munich scoring either side of the interval through Daniel Adlung and Bobby Wood.
West Ham endured further disappointment on their tour of New Zealand, with Sydney prevailing 3-1 to add to the 2-1 loss inflicted on Sam Allardyce's side by Wellington Phoenix on Wednesday.
Fellow Premier League outfit Newcastle United fared better against Wellington, winning 1-0, which was also the scoreline by which newly promoted Burnley beat League Two Accrington Stanley.
Hull City, who will embark on a maiden journey into European football this season, were held 1-1 in the slightly less glamorous surroundings of Barnsley.
Scottish champions Celtic also fell to defeat as Christopher Nothe scored the only goal of the game for St Pauli.
There were no such problems for Lazio, however, as Cristian Ledesma, Diego Novaretti and Felipe Anderson gave Stefano Pioli's side a 3-0 win over Perugia.
Andrea Stramaccioni collected his first win as Udinese boss thanks to goals from Allan and Alex Geijo in 2-1 win against Trapani.
Elsewhere, Real Sociedad beat NEC 1-0, Levante drew 1-1 with Vitesse, Paderborn lost 2-1 to Maccabi Haifa and Cologne went down 2-0 versus Ingolstadt.
Finally, Primeira Liga side Sporting had a comfortable afternoon thanks to goals from Andre Martins, Cedric and Jefferson against Utrecht.