Gremio consolidated third position in the Brazil Serie A after running out 1-0 winners over Ponte Preta on Saturday.
Former Hertha Berlin striker and substitute Andre Lima was the hero for the hosts, netting a 91st-winner as the 10 men of Gremio extended their unbeaten league run to 11 games.
Vanderlei Luxemburgo's side are a solitary point adrift of second-placed Atletico Mineiro with four games to play.
A hat-trick from Brazilian international Neymar inspired Santos to a thumping 4-0 victory against Cruzeiro.
With the two sides level on points heading in the match, bragging rights were at stake and it was not long before Santos broke the deadlock through Neymar on 12 minutes.
And the striker made it 2-0 with less than 10 minutes remaining in the first half. Felipe Anderson added a third for the visitors before Neymar completed the rout during the final eight minutes.
Meanwhile, Figueirense's survival hopes were dealt a huge blow after they were beaten 1-0 at Flamengo.
Substitute Hernane netted the match-winning goal on 72 minutes, having only been on the pitch for just over 10 minutes. Figueirense now languish in 19th position, eight points adrift of safety with fellow relegation-threatened clubs Palmeiras, Sport Recife and Bahia scheduled to play on Sunday.