With new goalkeeper David de Gea and defender Phil Jones making their debuts, United struggled for an hour and were fortunate only to concede through Cory Gibbs' early header.
But Rooney led the fightback, following up his hat-trick in Seattle by levelling in eye-catching fashion before Rafael and Nani ensured United remain on the winning road ahead of the greatest tour tests against an MLS All-Star team containing David Beckham and Thierry Henry in New York on Wednesday and then Champions League winners Barcelona next Saturday in Washington.
After the expected dominant start, United suffered a nasty shock after 12 minutes when Jalil Anibaba launched a deep free-kick into the penalty area.
Gibbs climbed above Jones close to the penalty spot and guided an excellent header into the bottom corner, with De Gea rooted to the spot.
It was the start of a disappointing half for Sir Alex Ferguson's men as Marco Pappa, Patrick Nyarko and Cristian Nazarit all wasted chances in what was by far United's worst 45 minutes of what has been an impressive tour to date.
They were indebted to De Gea right on half-time when he kept out a goalbound Nyarko effort with a smart feet-first save.
The nearest United had come was a shot that Gabriel Obertan screwed wide, whilst Dimitar Berbatov was marginally offside when he collected Tom Cleverley's chipped pass at the end of the visitors' best move, although Sean Johnson saved anyway.
Ferguson was presumably planning to make changes at half-time anyway and the five who came on, including Rooney for Berbatov, did strengthen the visitors.
Chris Smalling was denied a very well-taken goal by an offside flag but was exposed by Nyarko at the other end and Baggio Husidic wasted a glorious chance to score by tapping wide of an open goal at the far post.
Pappa then blasted a shot into the side-netting, which a sizeable proportion of the 61,000 crowd thought had gone in, before De Gea pushed a low Orr Barouch effort onto his post.
Needing some inspiration, it was no surprise Rooney provided it, anticipating Rio Ferdinand's lofted pass into the penalty area before brilliantly lobbing substitute goalkeeper Jon Conway.
Once level, there was only going to be one winner and a matter of seconds after being introduced for Smalling, Rafael surged into the box and finished superbly from an acute angle.
Nani produced an superb piece of skill to bag a third eight minutes from time.