كتب : Hatem Maher
The England midfielder, who joined Milan from LA Galaxy on a short loan deal, fired home from a tight angle in the 59th minute to make it 4-1.
Bologna took the initiative after just nine points when the league's top scorer Marco Di Vaio converted a penalty after Paolo Maldini brought down Christian Amoroso.
Clarence Seedorf equalized three minutes later with a rebound from seven yards out after Francesco Antonioli parried Kaka's shot into his path.
Brazilian playmaker Kaka, who accepted Milan fans' pleas to reject a big-money move to Manchester City, put the visitors ahead in the 17th minute.
He notched from the spot after Giancluca Zambrotta fell under a challenge from Davide Bombardini.
Bologna's hopes of grabbing the equalizer were dealt a blow when Gaby Mudingayi received his marching orders for a second bookable offense.
Milan made their numerical advantage count shortly after as Kaka got on the scoresheet again just before the break to finish off a swift move and add the third.
He gathered Alexandre Pato's deft back-heeled pass, skipped past a defender and fired a powerful left-footed drive from the edge of the area that left the keeper with no chance.
Beckham put the result beyond doubt with a smart finish after being fed by Seedorf.
Inter can move three points clear of Juventus and six ahead of arch-rivals Milan if they beat Sampdoria later in the day.