The French club, who won the inaugural edition of the Champions League in 1993, have now passed the previous record of 12 defeats in a row set by Belgian side Anderlecht between 2003 and 2005.
The Nigerian Zaidu Sanusi gave Porto the lead six minutes before half-time in a match played behind closed doors at the Velodrome.
Porto then had on-loan Liverpool midfielder Marko Grujic sent off midway through the second half but they went 2-0 up soon after.
Marseille defender Leonardo Balerdi gave away a penalty and was sent off for a second yellow card. Sergio Oliveira converted the spot-kick and the Portuguese club are close to joining Manchester City in qualifying from Group C with two games remaining.
In contrast, Andre Villas-Boas's pointless side are eliminated from the competition after four defeats out of four this season, but could still catch Olympiakos to take third place and salvage a place in the Europa League knockout rounds.
They host the Greek side next week before finishing their campaign away to City.
Marseille's current run started when they lost their last three matches in the 2011/12 competition, although they did make it to the quarter-finals in that campaign.
Then they lost all six group games in the 2013/14 season before returning to Europe's elite club competition this season after a seven-year absence.
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