Ajax named a strong team for the pre-season clash, with Frenkie de Jong - strongly linked with a move to Barcelona - operating alongside the much-coveted Matthijs de Ligt at centre-back. Klaas-Jan Huntelaar, meanwhile, led the line for the visitors.
Diogo Jota was next to try his luck with two separate attempts in the 18th minute, but his first from a corner was blocked, before Onana gathered the attacker's second effort.
Wolves continued to create the better openings and came close once again in the 32nd minute when Jota was released by Neves in a dangerous area, but Onana did well to claim.
It was Ajax that took the lead in the closing stages of the first half, however, when Donny van de Beek found space in a dangerous position before picking out the corner with a smart finish.
Helder Costa had the first half-chance of the second period when he collected a short free kick from Cavaleiro before striking towards goal, but Onana collected the deflected effort.
Daley Blind made his second Ajax debut as a second-half substitute following his move from Manchester United, and the Dutch outfit were using the ball well despite coming under pressure.
Jota headed over the Ajax goal on the hour as Wolves continued to press, before the 21-year-old forced a smart save from Onana 10 minutes later as chances continued to arrive.
The English side were finally level in the 74th minute, however, and it came from a Neves penalty after Costa had been brought to the ground inside the Ajax box.
Wolves, who came close to winning it late on with a Danny Batth header, will continue their pre-season preparations with a clash against Stoke City next Wednesday, while Ajax will face Walsall on the same night.
WOLVES (3-4-3): Norris (Ruddy 46'); Boly (Watt 84'), Coady (Batth 84'), Bennett (Saiss 72'); Giles (John 84'), Gibbs-White (Pereira 71), Neves (Hause 84'), Doherty; Cavaleiro (Ashley-Seal 71'), Jota (Mir 84'), Costa (Enobakhare 87')
AJAX (4-3-3): Onana; Kristensen, De Ligt, De Jong (Blind 46'), Tagliafico; Mazraoui (Jensen 88'), Eiting, Van de Beek (De Wit 79); Lang, Huntelaar (Sierhuis 84'), Neres