Skipper Jamaal Lascelles had headed the Magpies into a 52nd-minute lead at St James' Park but Neves levelled with an equally-impressive headed finish 17 minutes from time to ensure that the game – like the previous four between the two sides – finished 1-1.
However, both might have snatched victory in a late flurry during which Wolves defender Romain Saiss unwittingly blocked Joelinton's shot on the line and saw the ball spin agonisingly over before home keeper Martin Dubravka, restored to the starting line-up, turned substitute Fabio Silva's point-blank header on to the crossbar in stoppage time.
The home side started brightly and might have been ahead as early as the sixth minute when Jonjo Shelvey played a free-kick square for Joe Willock to pick out Isaac Hayden, who directed his header straight at keeper Rui Patricio.
Wolves were content to sit behind the ball when out of possession, but were almost made to pay for it when Miguel Almiron got in behind to run on to Shelvey's 12th-minute pass and shoot across Patricio, only to see his effort come back off the far post.
The visitors gradually eased their way into the game, but Patricio had to save from Emil Krafth and Joelinton in quick succession and then saw an Allan Saint-Maximin strike ruled out for offside after he had parried Willock's 24th-minute drive with the Magpies continuing to threaten.
Nuno Espirito Santo's men called upon Dubravka for the first time with 14 minutes of the first half remaining when the Slovakia international turned Adama Traore's header around the post, but the keeper was relieved to see Pedro Neto fire wastefully wide after Traore had breezed past full-back Krafth and squared.
Neto, who minutes earlier had tested Dubravka with a deflected shot from distance, drilled the ball across the six-yard box after leaving Jamal Lewis for dead on the stroke of half-time, but no team-mate could get a touch with the goal yawning.
The lively Almiron, who had received treatment on the pitch before the break, was notable by his absence after it with Ryan Fraser sent on in his place, but Wolves picked up where they had left off and Neves fired over following a flowing 50th-minute attack.
But it was the Magpies who made the breakthrough two minutes later when Fraser delivered an inviting right-wing cross to the near post, where Lascelles got ahead of defender Leander Dendoncker to thump a header past Patricio – his first league goal since October 2019.
Newcastle were dealt another blow with 28 minutes left on the clock when a hobbling Saint-Maximin followed Almiron down the tunnel, and they were pegged back within 11 minutes when Neves twisted to head Neto's cross firmly past Dubravka, who got a hand to the ball, but could not keep it out of his net.
The home side were desperately unfortunate not to regain their lead when Joelinton's goal-bound effort hit Saiss on the elbow before looping over, but they would have lost it at the death had Dubravka not managed to touch Silva's header on to the underside of the bar.