A typical poacher's goal by in-form Italy international Filippo Inzaghi edged out the Dutch giants, who came within seconds of knocking Milan out in last season's quarter-finals.

Inzaghi's second-half winner was his sixth in five games, having scored the winner in Milan's 2-1 win against Bologna on Saturday and four for Italy in their two recent Euro 2004 qualfiers.

Despite Milan's domination they had their Brazilian goalkeeper Dida to thank for denying Rafael van der Vaart an equaliser in stoppage-time with a breathtaking one-handed save.

Milan's victory was soured by the late sending-off of midfielder Gennaro Gattuso, who was red-carded for lashing out at Sweden international Zlatan Ibrahimovic.

Inzaghi refused to lap up all the applause for what was a solid team performance that should have reaped more goals.

"It's a magical moment, let's hope it continues," he said. "I dedicate the goal to all of my team-mates, even those who didn't play.

"We mustn't forget that there were great players on the bench like Manuel Rui Costa and Rivaldo."

Milan coach Carlo Ancelotti was disappointed with the way his team failed to kill off Ajax.

"We really should have had the game sewn up, but we wasted many chances and they nearly drew level right at the end," he said. "On another day we might not be so lucky."

Rui Costa was left out to accommodate Brazilian midfielder Kaka, while Tom Soetaers and Nigel De Jong, who played in the 4-1 league win at the weekend, were dropped to the substitutes' bench.

A surprisingly open first-half, lit up by a majestic performance from Kaka, failed to produce a goal, despite numerous openings for both sides.

The first opportunity fell to Van der Vaart whose rising drive was tipped over the bar by Dida.

The Italian hosts responded to the early scare and with Kaka pulling the strings on the left-hand side of midfield put Ajax's goal under siege.

Andriy Shevchenko volleyed wide after latching on to Andrea Pirlo's pinpoint cross, before Gattuso's venomous drive cleared the bar by inches.

Dida palmed away Ibrahimovic's angled header just after the half hour mark as Ajax interrupted Milan's spell of possession, while at the other end only a last-ditch tackle by Julien Escude denied Inzaghi a certain goal.

The first 45 minutes ended in controversy as Milan were denied what appeared to be a certain penalty.

Inzaghi danced his way through the Ajax defence and closed in on goal only to be sent tumbling to the floor by Petri Pasanen's clumsy challenge.

However the cheers of the home crowd were silenced as the referee waved play on, much to the annoyance of the Milan players.

Milan continued to dominate after the break and Shevchenko saw two early chances comfortably saved by Ajax goalkeeper Bogdan Lobont.

Steven Pienaar's goalbound flick was smothered by Dida before Milan took the lead in the 67th minute.

Inzaghi broke forward with purpose and fed Shevchenko, who turned his marker smartly before firing towards goal.

Lobont failed to hold the Ukrainian's powerful effort and Inzaghi was on hand to tuck the ball home.

Gattuso's 90th minute dismissal gave Ajax a numerical advantage and they almost cashed in through Van der Vaart's last-gasp effort only for Dida to come to Milan's rescue.

Last season Ajax were poised to go through to the semi-finals on the away goals rule until Jon Dahl Tomasson scored a late winner to clinch a 3-2 win at the San Siro after the teams had played out a goalless draw in Amsterdam.