The 36-year-old rolled back the years for the Brazilian side who trailed 3-1 at half time, in a top of the table clash against rivals Botafogo.
Former Liverpool ace Suarez, took just 19 minutes to net his hat-trick and turn the tide in favour of Gremio, who are now level on points with Botafogo at the top of Brazil's Serie A.
The Uruguayan appears to be doing all he can to bow out at Gremio with a first title since 1996 after coach Renato Gaucho revealed that Suarez would leave the club at the end of 2023.
Suarez has been linked with a reunion with ex-Barcelona teammates Lionel Messi, Jordi Alba and Sergio Busquets at Inter Miami as the MLS side continue to build a squad capable of competing for honours.
Before Messi's arrival in South Florida this summer, Beckham's Inter Miami found themselves rock bottom of the Eastern Conference but their fortunes quickly turned around thanks to Messi's influence.
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The MLS side brought in Gerardo Martino as coach replacing Phil Neville before Messi inspired his new teammates to success in the Leagues Cup - the first trophy in the franchise's short history.
But expectation will be different next season with Miami likely to be among the early-season favourites to win the MLS Cup.
Messi is believed to want Inter Miami to continue to strengthen with more former Barcelona stars.
In addition to Suarez, Miami could offer Sevilla midfielder Ivan Rakitic a fresh start in the United States with El Gol Digital reporting that Messi has asked Beckham to sign the Croatian.
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Rakitic existing deal expires in June 2024 but Inter Miami would need to sign him in January to avoid a clash of transfer deadline dates between MLS and European clubs.