Rome, Italy (AP) — Champions Inter Milan claimed derby honours by hammering city rivals AC Milan 4-0 after Gennaro Gattuso was sent off in the first half.

Milan, and Gattuso in particular, self-destructed in spectacular fashion during a 10-minute first half period in a match that suggests the loss of Kaka to Real Madrid has hit the red and black half of the city harder than they thought.

Thiago Motta scored his first goal for Inter and fellow new-recruit from Genoa Diego Milito added a penalty before Brazilian full-back Maicon's strike had all but ended the contest by half time.

Serbian Dejan Stankovic's second half rocket put the gloss on an accomplished performance as coach Leonardo suffered a miserable first derby in charge of Milan.

Leonardo claimed his team were well in the match until the first goal.

"For half an hour we played well and matched an excellent Inter team. But after the first goal we struggled to get a handle on the game. We still need to improve," he said.

Inter coach Jose Mourinho, who gave a debut to Dutch attacking midfielder Wesley Sneijder following his move from Real, had no desire to dwell on this victory.

"Tomorrow is another day, this is already finished," he said. "After the first goal it was no longer a contest and my team won easily."

Sneijder justified his manager's faith on six minutes, testing Milan goalkeeper Marco Storari with a curling effort from outside the box.

"It's always like that in football, we have to make our decisions and if you win you're fantastic but if you lose it's a disaster," added Mourinho.

"I knew if Sneijder didn't play well I would have been the target of criticism for picking him.

"But he played really well. Last week (after a 1-1 home draw with newly-promoted Bari) I was useless. Now I'm fantastic because I played him (Sneijder).

"It's the same thing for Leonardo, before he was fantastic (after winning 2-1 at Siena) and today he's poor. But he should keep the faith."

On 13 minutes Ronaldinho should have done better when teed up by Pato but after skying his shot miles off target and falling over in the process, the Brazilian tried claiming a penalty despite there being no contact from Stankovic when he tripped over his own feet.

Milan looked lively at that time but the first goal on 29 minutes changed everything.

It came from a sweeping team move on the edge of the Milan box as Motta fed Samuel Eto'o, who shifted the ball on to Milito before the Argentine played the ball behind the backline where Motta, who had continued his forward run, unchecked by either Mathieu Flamini or Marek Jankulovski, curled a shot beyond Storari.

Six minutes later and Milan fell to pieces.

From a Milan free-kick Inter broke at pace with Maicon lumping a long ball down the line for Eto'o to chase. The Cameroon forward skinned Gattuso who slung his arm around the Inter man's neck and hauled him down inside the box for a clear professional foul.

Inexplicably the referee only showed Gattuso a yellow card but Milito exacted adequate punishment by smashing his penalty home, straight down the middle.

Captain Gattuso had already signalled to the bench that he wanted to come off before the goal but his attempts to leave the field were hampered as substitute Clarence Seedorf wasn't ready.

Play continued and on 40 minutes Gattuso hacked down Sneijder, earning a second yellow before Seedorf had a chance to enter the fray.

Gattuso was irate and blasted his bench as he trudged off, leaving his team a man down.

Leonardo admitted he messed up on the substitution.

"Of course I made a mistake in not making the substitution sooner but Seedorf wasn't ready to come on, partly because he had some ice on his calf due to a slight muscle problem," he explained.

To add insult to injury, Maicon scored a third on the stroke of half-time after a one-two with Milito as Flamini once again failed to track a forward run.

Stankovic's howitzer from 25 yards halfway through the second period was the final nail in Milan's coffin but tellingly, the nominal hosts at the San Siro -- a ground the two teams share -- had a hand in their own downfall as Andrea Pirlo failed to close down the Serbian, giving him time and space to pick his spot.