The Colombian's header cancelled out Roman Kienast first-half strike as Porto missed a chance to overtake second-placed Zenit St Petersburg, who earlier drew 1-1 against group winners Atletico Madrid in Russia.
With one round to go, the Portuguese side remain third on five points, one behind the Russians. Atletico are top with 13 points while the Austrians, who will finish bottom, have only two and cannot qualify for the Europa League.
Champions League debutants Vienna surprised experienced Porto after 11 minutes when Kienast collected the ball in midfield, dribbled past two opponents and drove a diagonal shot from outside the box off the ground and into the net.
Porto hit back through Martinez, who headed in from close range shortly after the start of the second half. Though they threatened several times after that, Porto failed to break the Austrians' resolve.
Vienna goalkeeper Heinz Lindner shone and Kienast made history for his club, netting the Austrians' first goal in this season's competition.
Lindner kept out a dangerous header from Martinez with a reflex save and won a series of one-on-ones with the Colombian and also against Steven Defour and Lucho Gonzalez.
Porto still took heart from Martinez's easy goal, his 12th of the season, which came after Mangala bravely won the ball from a corner.
But the Portuguese failed to grab the winner as substitute Silvestre Varela and Martinez missed excellent chances.
Porto finished the match with 13 shots on goal compared to the Austrians' two.
Although they can still qualify, the result extends Porto's dip in form. Ahead of Tuesday's stalemate, the Portuguese champions had two consecutive draws in their domestic league.
(This version of the story makes it clear in paragraph six that Vienna scored their first goal in this season's competition.)
(Writing by Daniel Alvarenga in Lisbon, Editing by Tony Goodson)
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