The English Premier League side, playing in their first European campaign since 1981, went ahead through an own-goal from Gleison Bremer just before half-time.
Diogo Jota made it 2-0 on the hour mark but Lorenzo de Silvestri pulled one back for the Italians two minutes later.
Raul Jimenez restored Wolves' two-goal lead after 72 minutes before Andrea Belotti's penalty for Torino in the dying moments kept the Serie A side in the tie ahead of the return leg at Molineux next Thursday.
Celtic, dumped out of the Champions League last week by Cluj of Romania, saw off AIK of Sweden 2-0 at home.
James Forrest scored in his fifth consecutive game early in the second half with Frenchman Odsonne Edouard's curling free-kick making it 2-0 in the 73rd minute.
"It was a great team performance," said Celtic manager Neil Lennon.
"We played well in the first-half but I thought we were magnificent in the second.
"Some of the football we played was great and we scored fantastic goals."
Glasgow rivals Rangers are also well-placed for a spot in the group stages thanks to a 0-0 draw at Legia Warsaw.
Elsewhere, there were convincing 3-0 home wins for Dutch sides Feyenoord and PSV Eindhoven over Hapoel Beer-Sheva and Apollon respectively.