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Hugo Ekitike put PSG ahead inside five minutes at Parc des Princes as the 20-year-old continued his recent form in front of goal, before Messi clinched the points with just under 20 minutes to go with a typically stylish finish as the defending champions extended their lead at the top of the league to six points.
After being beaten 3-1 in their previous league outing by title rival Lens, Christophe Galtier was able to recall Messi and Neymar back into the team for the visit of bottom-of-the-table Angers.
Abdel Bouhazama did not name star players Azzedine Ounahi and Sofiane Boufal in his starting XI, with both being linked with moves away in the January transfer window, though the latter came off the bench for the final half-hour.
After a minute's applause was observed to pay respect to the late Pele, PSG started with intent as Ekitike swept Nordi Mukiele's low cross from the right past Angers goalkeeper Paul Bernardoni to score in his third-consecutive game.
It should have been 2-0 midway through the first half when Sergio Ramos got on the end of a Messi free-kick, only for Bernardoni to make a smart save from the Spaniard's header, before also denying Messi with a stop to his left just after the half-hour mark.
Angers started the second half well as PSG struggled to put the game to bed, and Abdallah Dipo Sima should have done better when in acres of space on the right of the hosts' penalty area on the hour, but he blazed his shot over the bar.
Messi had a nervous wait to see if he had doubled the lead in the 72nd minute after he ran onto a Mukiele pass to roll the ball into the bottom-left corner of the net, with a VAR review eventually overruling the initial decision of offside, much to the Argentine's delight and PSG's relief.
