Goals from Quinton Fortune and Cristiano Ronaldo saw off a poor Everton side with the minimum of fuss as ugly behaviour from the crowd marred a cup-tie fought in a good spirit.
United boss Sir Alex Ferguson, as expected, selected in-form Rooney to lead the line, as Everton struggled for striking cover in his absence. James Beattie was suspended and Duncan Ferguson injured.
Contrary to his manager's insistence that Rooney's temper would not be an issue, the teenage striker started a confrontation with a woman sponsoring the match, at pitch side.
He then launching into a snarling exchange of words with the crowd. And this was before the warm-up was complete.
Rooney's temperament may be in question, but the teenager's nerve certainly isn't.
Minutes into the contest, as his every touch was greeted by a deafening crescendo of insults, Rooney won a throw-in near the corner flag. Rather than keep his distance he patiently waited for the ball, while objects from the stands rained down.
But it was his former team-mate Leon Osman who lifted the home fans further by sneaking inside Roy Keane to fire in a shot that sped just wide. On 13 minutes
Marcus Bent then had a header cleared off the line by Gabriel Heinze from Kevin Kilbane's corner.
The Argentine then fed Rooney with a beautiful slide-rule pass, but a fine block from Alan Stubbs prevented the home fans' nightmare coming to fruition.
A surging run from Fortune on 20 minutes presented United with a golden chance to break the deadlock, but Nigel Martyn came to the rescue with a fine save, as Rooney waited to pounce.
Fortune wasn't to be denied a minute later as a magnificent cross by Ronaldo allowed the South African international to rise unchallenged to nod home.
United killed the rest of the half in a manner Ferguson's side has made its own. Through the inspirational Keane they passed and passed and the Everton fans, who seemed more interested in booing their former hero than getting behind their team, were silenced.
Bent had a great chance the level the scores two minutes before the interval when he beat the offside trap to create Everton's first clear sight of goal. But the former Ipswich star's abysmal first touch allowed Roy Carroll to snuff out the chance with relative ease.
United came close to doubling their advantage but Martyn, who saw the ball late, tipped Ronaldo's swerving effort around the post. Rooney's fine control gave him an excellent chance to ram the taunts down the throats of his former paymasters, but as blue hearts jumped into aching throats, Martyn again came to the rescue to make a fine stop from the half-volley.
Ronaldo secured United's place in the last eight after 57 minutes after Paul Scholes' bullet free-kick - incidentally won by the Portuguese trickster – when he mopped up Martyn's messy parry.
With no hope of getting back into the game, the hapless Everton fans returned to their abusive best as chants echoed from the stands. But just like their team, they were beaten.
They disgraced themselves further by striking down United keeper Carroll with a mobile phone launched from the crowd.
But Rooney left his former home with his head held high. His temperament stood up to its biggest test and if he ever felt bad about leaving, those thoughts would have been utterly dispelled by the final whistle. But to be honest, he had a quiet game.
MAN OF THE MATCH: Roy Keane (Manchester United) – Back to his imperious best, the United captain controlled the match with yet another superb individual performance.