Experienced goal-poacher Inzaghi, carelessly left unmarked at the far post, put the visitors ahead on 28 minutes when he tapped in from close range after a perfect cross by playmaker Clarence Seedorf.
Marseille recovered to level four minutes into the second half, Argentina defender Gabriel Heinze heading home from a Benoit Cheyrou free kick.
Inzaghi, however, was on target again on 74 minutes, converting another fine Seedorf pass with perfect timing to present the visitors with victory on a rainy night in the Mediterranean port city.
Milan coach Leonardo lost his voice and skipped the post-match news conference, leaving assistant Mauro Tassotti to say how pleased he was.
"This was a good show from us, especially in the first half, and this is a good result but it's too early to say we're back," Tassotti said. "What we need is a string of good results."
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Marseille, who beat AC Milan 1-0 in Munich in the inaugural Champions League final in 1993, suffered at first against opponents better organised but then woke up and the second half was lively and largely in their favour.
"Tonight we saw the difference between a good French team and a great European side," Marseille defender Souleymane Diawara told reporters.
"We were inattentive twice and they scored two goals. We will learn from this for our next matches," he added, looking forward to matches against Real Madrid and FC Zurich.
The home side had hardly created a chance until midfielder Cheyrou fired from the edge of the box just before halftime, requiring a perfect save from Milan keeper Marco Storari.
Marseille came close again early in the second half with an angled shot from just outside the area by Argentina midfielder Lucho Gonzalez and levelled just after that.
Looking more and more confident, Marseille went on to create a few more chances but the Milan defence held tight and then Inzaghi lived up to his reputation as one Europe's most-feared marksmen.
The match was tense and marred by a few ugly scenes, notably a dangerous tackle from Milan's French midfielder Mathieu Flamini. The former Marseille player was lucky to escape with just a yellow card for his second-half challenge on Stephane Mbia.
