But rather than folding, Milan came back strongly, with Inzaghi denied once again by the frame of the goal from a diving header.
On came Ronaldinho, who quickly made an impression when he curled in an exquisite 25-yard free-kick to give Milan a lifeline.
Luca Antonini went close with a low, skidding shot as the visitors searched for an equaliser, which they got when Inzaghi struck after his sublime first touch set him up to earn his side a vital point.
It was a hugely disappointing end for Pompey and their fans, but the club still has hopes of making the last 32.
They need to pick up points from their remaining games against Germany's Wolfsburg - away next Thursday - and Holland's Heerenveen to join Milan in the group's top three.
Portsmouth manager Tony Adams:
"The boys are feeling flat in there. They thought they had won it. But I'm proud of them tonight.
"This was the best performance I've seen from us in a long time. And we can still say we are four games unbeaten now, including against Milan.
"We are struggling to put teams to bed, but they (Milan) have some excellent players. If you switch off, they punish you.
"We can work on picking teams up from set plays but it was a fantastic free-kick. But I was very entertained by my players tonight.
"We've given ourselves a chance but we will still have to get over this. The boys are really upset they didn't hang on to win."
Milan coach Carlo Ancelotti:
"Ronaldinho's free-kick changed the face of the game but we almost lost hope. The reaction had to be good and it was, but you don't often get the opportunity from 2-0 down.
"We were a little lucky. We played quite well in the first half but it became a bit more difficult in the second half after they took the lead.
"Inzaghi deserved his goal. He was unlucky to twice hit a post but we still had to get the break to recover.
"(Portsmouth's) performance did not surprise me. I think they can still go through to the third round in the UEFA Cup with us."
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