After Ruben Semedo's first-half red card, Youssef El-Arabi put the hosts ahead in front at Georgios Karaiskakis Stadium, with Friday's (AEDT) game being played behind closed doors because of the coronavirus outbreak, Olympiacos owner Evangelos Marinakis having tested positive.
In a pre-match interview with BT Sport, Wolves boss Nuno Espirito Santo said the decision to play the game was "absurd", and his side delivered a flat performance, although Neto's fortuitous strike earned a potentially decisive away goal.
UEFA is set to rule on whether the UEFA Europa League will be postponed amid the crisis, but the second leg is set for next week as it stands.
Giorgos Masouras clipped the crossbar with a poor early effort, but the offside flag was raised regardless, and Olympiacos was then reduced to 10 men in the 28th minute.
Wolves broke at pace down the left, and Semedo clumsily brought down Diogo Jota on the edge of the box, prompting referee Clement Turpin to show the red card.
Neto replaced Matt Doherty in an attacking half-time change for Wolves, but the 10 men took the lead in the 54th minute.
Guilherme jinked into the right side of the box and squared for El-Arabi to tap in his 19th goal of the season from close range.
Wolves levelled 13 minutes later, though, Neto's free-kick taking a huge deflection off Andreas Bouchalakis to beat Jose Sa, who earlier blocked a ferocious Raul Jimenez drive with his face.
Nuno sent on ex-Olympiacos star Daniel Podence in search of a late winner, but the tie remains finely poised.