Wolves' Diogo Jota struck either side of quickfire goals from Maupay and Propper in a crazy 16-minute spell at the end of the first half.
Brighton's encouraging start to the season continued as they moved level with Arsenal, while another point on the road lifted Nuno Espirito Santo's spirited side back up to sixth.
Maupay said, "It was a tough game for us, the third game of the week is never easy, especially against a good team.
"We didn't start very well and gave chances away, but we kept pushing and scored two goals.
"I thought we were going to win because we were back in the game with the crowd pushing us. But we made a mistake for them to score the second goal.
"We had a couple of chances in the second half. We're not happy but we will take it. Overall I think it is a good point.
"We were a bit tired and missed a bit of sharpness."
Brighton, still buzzing after Thursday night's memorable win over the Gunners, almost scored in the opening seconds.
Leandro Trossard stood up a tempting cross, Steven Alzate's header was blocked and Maupay's deflected effort went over, before Lewis Dunk headed the resulting corner narrowly over.
Wolves responded through a Ruben Neves drive which flew inches wide and Seagulls keeper Mat Ryan made a fine save to keep out a header from Romain Saiss.
The visitors should have gone ahead after Adam Webster dallied on the ball in his own penalty area and was pickpocketed by Jota.
Jota squared the ball to Raul Jimenez but just as the Mexican shaped to shoot Dunk got a foot in.
Moments later the same duo combined to fire Wolves in front. Jota collected the ball on halfway, sent Jimenez down the left and then raced into the area to meet the cross and sidefoot home.
Jota was denied a second by Ryan after racing through one-on-one, and the miss quickly proved costly when Brighton launched an astonishing turnaround.
First Maupay latched on to a ball over the top from Dale Stephens and crashed a superb first-time shot inside the near post.
Then Wolves, who moments earlier had been in cruise control, were stunned again 90 seconds later when Trossard pulled the ball back and Propper thumped his header home.
It was Dutch midfielder Propper's first home goal for Brighton, more than two years after joining the club, but it took him just eight minutes to cancel it out as a breathless first half came to a close.
Propper's blind pass sideways rolled straight to Jonny, who was able to slip in Jota for his second to equalise.
After the break Dunk survived a VAR check after blocking Jota's close-range shot, with Wolves claiming a handball which would have been harsh.
Wolves could have snatched the win late on when Patrick Cutrone reached the byline and pulled the ball back but fellow sub Pedro Neto was unable to provide the finish.