Gustavo Manduca struck on 90 minutes to send 25,000 fans into raptures after Porto, who were surprisingly held 1-1 by APOEL in Portugal last time, thought they had grabbed a point thanks to Hulk's 89th minute penalty.
Ailton's 42nd minute spot-kick had given the impressive Cypriots the lead.
APOEL, rank outsiders before the competition, head the group by a point from Zenit St Petersburg with two matches left and a win at the Russians on November 23 will sensationally send them to the knockout stages and guarantee them top spot with 11.
Zenit beat bottom side Shakhtar Donetsk 1-0 earlier on Tuesday.
APOEL coach Ivan Jovanovic said he would happy finishing third in the group and dropping into the latter stages of the Europa League, a mark of what an amazing feat it would be for the small club if they progressed in the Champions League.
"At this stage we are very close to the Europa League and it seems we are going to play in Europe until March," the down-to-earth boss told reporters.
"As for the Champions League we will try to achieve it. It will be great but still we have a way to go. My wish is that my players will keep playing with the same passion in the remaining two matches. If we do it, and it is up to us, then we have chances to do many things."
Porto, the Europa League holders who last won the Champions League under Jose Mourinho in 2004, stay on four points from four games and are scrambling to salvage their last 16 hopes. They next travel to Ukraine to play Shakhtar.
"It was a complicated match. The first half wasn't well played. We had the will to win and put in many crosses but had few clear chances and ended up conceding," Porto coach Vitor Pereira told reporters.
"The second half was different, we created chances and made it 1-1. After that, a team with our experience, that won the Europa League, should have settled down and not got carried away emotionally.
"We should have used our heads more but we lost balance as a team and got punished," added Pereira.
"We still depend only on ourselves and must now win the next two matches to qualify."
STOUT DEFENCE
Porto controlled the game for the first 20 minutes but were kept to shots from distance.
APOEL struggled to get organised in midfield and Ailton wandered offside four times.
Hulk then nearly scored from close range while a minute later the home side's Ailton had a diving header saved.
Porto then had another chance in the 38th minute when Kleber found himself completely unmarked in the box but he was slow to react and the ball was cleared.
Two minutes later APOEL were awarded a penalty when Ailton was brought down in the box by Eliaquim Mangala.
Ailton stepped forward and made no mistake from the spot.
In the second half, Porto threw everything into attack but striker H
