Manchester City now trail Liverpool by 10 points.
Mohamed Salah has scored 50 goals for Liverpool quicker than any other player in the club's history after just 65 appearances for the Reds.
Jurgen Klopp put Firmino on the bench but brought him on with about 20 minutes to go.
Roberto Firmino scored a stoppage-time winner to hand Liverpool a 3-2 win over PSG in their opening Champions League match.
Despite late drama, victory was well deserved for Liverpool who dominated throughout and bounced back from blowing a 2-0 first-half lead.
Brazil, playing their first international since a disappointing World Cup quarterfinal exit, were in complete control throughout a low-key encounter at the MetLife Stadium.
Mohamed Salah got Liverpool up and running as they comfortably dispatched West Ham in their first Premier League fixture of the season.
Brazil overcame a tricky start to the last-16 tie, as second-half goals from Neymar and Roberto Firmino sealed a deserved victory.
Neymar scored the first goal in the 51st minute. Roberto Firmino then scored in the 88th minute to seal the win for Brazil.
Steven Zuber powered home an equaliser from Xherdan Shaqiri's corner five minutes after the break.
Neymar, the world's most expensive player following his blockbuster move from Barcelona last year, had been sidelined since the end of February when he fractured his foot playing for PSG in a league victory against Marseille.
Klopp's men started their Champions League campaign in a playoff against Hoffenheim just to make the group stages back in August.
Neymar's returning form will be a key factor for the team, which lost influential right-back Dani Alves to a knee injury last week.
Liverpool, inspired by two-goal Egyptian Mohamed Salah, took a big step towards the Champions League final with a 5-2 win over AS Roma in their semi-final, first leg at Anfield on Tuesday.
Liverpool moved a step closer to securing Champions League football next season via a top-four finish.
Liverpool moved back above Tottenham Hotspur into third and to within two points of bitter rivals Manchester United in second.
Jay Rodriguez scored twice as West Brom pulled off a thrilling 3-2 victory at Liverpool in the fourth round of the FA Cup.
Liverpool are beginning to develop impressive momentum and have now collected 16 points from their last six league games.