All four teams can still progress from Group C and the winner of Leicester's game against Legia Warsaw at the King Power Stadium on Thursday would replace Spartak at the summit.
After a fast start to the season, Napoli are now winless in three games in all competitions after taking just one point from their last two Serie A matches.
Russian international Sobolev gave Spartak, who lost 3-2 in Naples earlier in the campaign, the lead with a third-minute penalty before netting again before the half-hour mark.
Eljif Elmas pulled one back for the visitors in the second period, but Napoli could not find an equaliser. Luciano Spalletti's side slip below Spartak on head-to-head away goals.
Standout matches today