Brighton were 1-0 behind and down to 10-men after injuries to Jeremy Sarmiento, Adam Webster and Adam Lallana.
Maupay, who was heavily criticised after the 0-0 draw with Leeds United for missing chances, produced a remarkable instinctive finish as he fired home an overhead kick from substitute Tariq Lamptey's cross
Soucek had earlier netted after just five minutes as the Czech international rose highest in front of Albion goalkeeper Robert Sanchez and glanced home his header from a dangerous inswinging corner.
Albion dominated possession and fashioned two decent chances in the first half. Maupay's was the more difficult as the Frenchman swivelled and dragged his effort just wide.
Jakub Moder also had a shot saved from Fabianski when the Poland international was clean through on goal and the experienced Lallana wasted a glorious opportunity on 67 minutes as he shot wide.
Scroll down and click through to see who shone and who struggled for Albion at the London Stadium