The storm had already claimed the lives of at least two people in China's Hainan and 16 people in the Philippines
The 21-year-old Spaniard, who had a miserable start to the season after joining from Osasuna for a 7-million euro transfer fee, poked the ball home on the hour in a lively encounter at the Stade Velodrome.
Marseille, with a mostly reserve team, were caught cold as Monaco went ahead in the 22nd minute when Mathieu Coutadeur converted a penalty after Brandao had handled.
The hosts piled on the pressure and levelled three minutes before halftime, with Ghana forward Andre Ayew heading home from a neat Benoit Cheyrou cross.
Marseille pressed hard after the break and Azpilicueta, who had scored an unfortunate own goal in his team’s 1-0 defeat against Spartak Moscow in their Champions League opener, scored his first goal for the Provence side.
The Spaniard then cleared off his goalline in the closing stages of the game.
Earlier, Paris St Germain recovered from a poor start to ease into the last four with a 3-1 win at Valenciennes.
Mathieu Dossevi opened the scoring for the northeners after only three minutes but PSG reacted swiftly as defender Zoumana Camara headed home from a free kick six minutes later.
Christophe Jallet doubled the tally with a low crossed shot in the 26th minute and Peguy Luyindula put the result beyond doubt six minutes into the second half.
Montpellier also reached the semi-finals when a Hasan Salih Kabze double gave them a 2-1 home victory over Lille. Auxerre reached the semis with a win over St Etienne on Tuesday.
The storm had already claimed the lives of at least two people in China's Hainan and 16 people in the Philippines
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Traffic will be diverted to the opposite side during this period