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PSG looked to hit back as Cavani played in winger Jeremy Menez, who opened up his body to unleash a tame shot that was easily stopped by the goalkeeper.
Cavani wasted a great chance as the visitors threatened on the counter when he decided to try to get a shot away instead of passing to a teammate in acres of space.
The home side almost made them pay minutes later as Nicolas Gaitan found space before crashing in a fierce strike towards goal, which bent just wide of the far post with the goalkeeper looking beaten.
However, PSG took the lead in the 37th minute as Menez controversially collected the ball in a dubious offside position, before laying it back for Cavani to tap home.
The visitors' lead did not last for long, though, as Lima powered home a shot just before the break to bring things level at half time.