Nicky Butt fired the hosts ahead before Gary Neville's own goal levelled the scores but efforts from Kleberson and David Bellion handed United another three points in the defence of their crown as Duncan Ferguson headed a late consolation.
Sir Alex Ferguson opted to ring the changes to his side and dropped Paul Scholes, Ryan Giggs and Ruud van Nistelrooy to the bench and also gave captain Roy Keane and midfield cohort Phil Neville the day off.
United dictated the tempo from the off and Cristiano Ronaldo tested Nigel Martyn's handling skills in the wet conditions early on with a diving header from Diego Forlan's cross.
On nine minutes, the champions forged ahead when Kleberson's cross was headed out only as far as Butt, who unleashed a fearsome volley which flew under the hands of Martyn.
But Everton were level in a matter of minutes, albeit in fortuitous circumstances, as Thomas Gravesen's superbly whipped in free kick was headed beyond Tim Howard by Neville.
With so many changes to their line-up, United were occasionally ragged although Forlan was proving a threat with his movement and had a header pushed over by Martyn and then steered a snap shot over the bar.
Everton largely relied on the long ball pumped in the direction of Kevin Campbell, who had little support with Wayne Rooney deployed on the right flank.
The Red Devils stole the lead again just before the break when Neville atoned for his earlier gaffe by delivering a pinpoint cross for Brazilian midfielder Kleberson to head past the helpless Martyn.
Kleberson's goal appeared to knock the stuffing out of the visitors, who struggled to inject any fluency into their attacking play after the interval and justly survived vociferous cries for a United penalty after Ronaldo tumbled under a magnificently-timed tackle from Tony Hibbert.
By that point, United had introduced Scholes as the hosts peppered Martyn's goal with shots from Ronaldo and Forlan.
Ronaldo's trickery proved too much for Hibbert and then Rooney, who was booked for a callous challenge, before the Portuguese winger chipped the ball to the far post for Bellion to head over when he should have scored.
On 68 minutes, though, Bellion made no mistake after Everton failed to clear the danger. Ronaldo's cross took a slight deflection into the Frenchman's path and he smashed the ball in from close range.
Everton followed up the introductions of Ferguson and Francis Jeffers by throwing on James McFadden and the Scotland international tested Howard with a well-struck shot while Ferguson crashed a shot into the side-netting.
The Toffees set up a tense climax to the contest when Ferguson - who has a fine record against United - stooped low to head in at the far post but it merely proved a consolation.
