There was drama in added time as Nantes centre-back Diego Carlos was sent off by Tony Chapron for appearing to accidentally trip up the referee, with the official responding by kicking out at the Brazilian and brandishing a second yellow card.
Players told French television after the game that Chapron claimed he had slipped and not kicked Carlos on purpose, despite clear video evidence to the contrary.
Di Maria poked in a 12th-minute opener for the visitors, before producing a glaring miss later in the first half.
Unai Emery's visitors took full advantage of their good fortune, and draws for Monaco and Lyon earlier in the weekend, to move 11 points clear at the top of the table.
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"It was different to lots of (our) matches," said Emery.
"This was a difficult team that put a lot of pressure on us. It's true that in the second half they pushed more... But I think the win is deserved."
Claudio Ranieri's Nantes stay fifth, eight points adrift of fourth-placed Marseille.
"Sala comes from behind and the goal was valid. But that's football."
World-record signing Neymar missed out for PSG with a rib problem but Edinson Cavani returned from injury, looking for the two goals he needed to break Zlatan Ibrahimovic's club goalscoring record.
Argentinian international Di Maria took advantage of Neymar's absence as he gave PSG the lead with his seventh goal of the season.
The front three were all involved as Cavani played a pass into Kylian Mbappe, and the teenager let the ball run for Di Maria to divert past Nantes goalkeeper Ciprian Tatarusanu.
Nantes continued to plug away and came close to a leveller early in the second period, but Sala was denied by a sprawling Alphonse Areola after latching onto a slack Layvin Kurzawa backpass.
- Sala effort ruled out -
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PSG almost took full advantage as Mbappe led a rapid breakaway, with Di Maria again the guilty party as he sliced horribly wide from the winger's cutback.
Ranieri's Canaries continued to trouble the runaway league leaders and Argentinian striker Sala glanced home a header from a free-kick, only to be flagged offside despite clearly being behind the last defender when the ball was played.
Earlier yesterday, Lyon failed to take second spot after being held to a 1-1 home draw by Angers, despite a goal from Nabil Fekir.
Monaco's goalless draw at Montpellier on Saturday handed Lyon the chance to leapfrog the principality club.
Karl Toko Ekambi gave the lowly visitors a shock 14- minute lead from the penalty spot, but the in-form Fekir dragged the hosts level shortly after half-time with his 14th league goal of the season.
"We're very disappointed, we had a bad start to the match and a difficult first half," said Fekir.
Saint-Etienne ended a 10-match winless streak with a 2-0 win over Toulouse thanks to goals from Robert Beric and Assane Diousse.