However, the game turned on a tale of two penalties, with Di Maria failing to make it 2-0 from 12 yards before former PSG midfielder Christopher Nkunku levelled in the 41st minute.
Leipzig were then given a chance to complete the turnaround from the penalty spot and it was one Emil Forsberg did not waste, sealing a victory that moves them level on points with group leaders Manchester United and three points clear of PSG, who finished the game with nine men after Idrissa Gueye and Presnel Kimpembe were sent off.
Careless defending from Dayot Upamecano gifted PSG the opener after five minutes, Moise Kean intercepting his attempted backpass and deftly playing in Di Maria to break the deadlock.
Only a tremendous double save from Keylor Navas prevented Leipzig from levelling almost immediately as Amadou Haidara and Angelino were denied from close range in quick succession.
Yet Leipzig continued to look extremely vulnerable at the back and were thankful to Peter Gulacsi for preserving a one-goal deficit as he got down low to keep out Di Maria's spot-kick after Upamecano handled Kean's shot in the area.
Di Maria and Kean each had the ball in the net but saw goals ruled out for offside and PSG's inability to punish Leipzig's poor play at the back proved costly when Nkunku rifled into the bottom-left corner from the edge of the area.
A great run down the left from Forsberg ended with him blazing over the bar but he did have the decisive say in the 57th minute, sneaking his penalty into the bottom-left corner after Kimpembe handled a ball into the PSG box.
Gueye received a second yellow for fouling Haidara in a battle for a 50-50 ball and PSG's frustrations were heightened late in stoppage time when a cynical foul saw Kimpembe given his marching orders for his second bookable offence.