Schalke plunder victory at Arsenal fortress
Dutchman Huntelaar rifled a shot past keeper Vito Mannone with 14 minutes remaining to give the Bundesliga side the lead their impressive performance deserved.
Afellay then sent the home fans heading for the exit doors when he sealed victory late on.
The Londoners, who had won their opening two games in the group, were subdued throughout as Schalke, semi-finalists two seasons ago, carved out the better chances.
Schalke have seven points from three games, one point ahead of second-placed Arsenal.
In his programme notes Arsenal manager Arsene Wenger described his side as having had "illusory possession" in the 1-0 defeat at Norwich City at the weekend.
They again flattered to deceive against Schalke in a sterile first half.
Missing the pace of the injured Theo Walcott and Alex Oxlade-Chamberlain and with Santi Cazorla struggling to impose himself in midfield, the home side hardly tested keeper Lars Unnerstall before the interval.
Gervinho almost got on the end of a Lukas Podolski cross early on and the Ivorian wasted a chance when he beat the offside trap but stumbled as he tried to cut in towards goal.
After a conservative start the visitors began to sense Arsenal's unease and began to make inroads.
They could have had a penalty after 14 minutes when Affelay appeared to have his ankles clipped by Mannone as he raced into the area.
Much to the disgust of Schalke coach Huub Stevens, Affelay received a yellow card for diving.
Peruvian Jefferson Farfan twice elected to pass rather than shoot and moments before the interval Huntelaar wasted a golden opportunity, shooting hopelessly wide of a yawning goal when set up by Atsuto Uchida's low cross.
Kicking towards their fans Schalke began the second half brightly but were guilty of more profligate finishing when Farfan cut a low pass back to captain Benedikt Hoewedes inside the penalty area but he scooped his shot over the crossbar.
Arsenal looked in real danger of losing to non-English opposition at home in Europe for the first time since 2003 - a run of 45 matches - as Schalke continued to threaten with Farfan finding acres of space down the right.
The Londoners sent on Olivier Giroud for Gervinho to try and grab a winner but instead it was Schalke who made the breakthrough with 76 minutes on the clock.
Afellay's header caught the defence flat-footed and Huntelaar this time made no mistake, slamming a shot into the net to send the fans behind the goal into wild celebrations.
Victory was secured in the 86th minute when Farfan escaped his marker down the right and provided Frenchman Affelay with an unmissable opportunity.
It completed a miserable night for Aresnal who last tasted home defeat in the Champions League against Manchester United in the 2008-09 semi-finals.
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