The Bundesliga side snatched victory in Group G thanks to an Eric Maxim Choupo-Moting spot-kick three minutes into stoppage time after Jonathan Silva had been wrongly penalised for handball.
Television replays showed that Huntelaar's header hit Silva in the face, but referee Sergey Karasev - who had earlier sent off Sporting defender Mauricio - pointed to the penalty spot.
Sporting had opened the scoring through Nani before Chinedu Obasi, Huntelaar and Benedikt Howedes netted for Schalke.
The visitors fought back through two goals from Adrien Silva, the first a penalty, only to be denied by that late decision.
"Today we were very lucky," said Huntelaar. "We were leading 3-1 with 11 players against 10 but then we gave it away. You don't normally win matches like this."
Defender Howedes echoed those thoughts when adding: "Only the three points count but, to be honest, it was a lot of luck.
"Seconds before the end it didn't look like this would be a great evening, but we never gave up."