Brighton took the lead in the first half through Aaron Connolly but a header from Romain Saiss and an own goal from Dan Burn gave Wolves the advantage.
It got worse for Burn and Brighton soon after as Burn clattered into Adama Traore in the box and Neves converted from the spot.
Albion were handed a lifeline just after the break as Joao Moutinio fouled Maupay in the box and the Albion striker confidently fired home the penalty.
Skipper Lewis Dunk gained a crucial point for the home team with a 70th minute header.
Scroll down and click through to see how the Albion players rated.
1. Robert Sanchez 6/10
No chance with the first that looped over him. For the second Sanchez saved Neto's deflected effort but it hit Burn and rolled into the net for an OG. Could do little with the Neves penalty.
2. Joel Veltman 6/10
Brighton have missed Tariq Lamptey on the right. Veltman was solid defensively and decent in possession without being spectacular
3. Adam Webster 8/10
Played a huge part in Albion's opener as he surged forward from defence. Great block on Silva when the scores were at 3-2. Unlucky with a header that crashed back off the bar
4. Lewis Dunk 8/10
Excellent header, albeit deflected, to make it 3-3. The passion in his celebration was great to see. Two goals in three matches for the inspirational skipper. Excellent in both boxes.