The victory takes them five points clear of Flamengo with two games remaining. The Rio club beat Gremio 2-0 to keep their slim hopes alive.
Borja missed a sitter for Palmeiras in the first half and Deyverson had a goal ruled out for offside before they finally got their breakthrough in the 58th minute when a defensive clearance bounced off Luan and into the net.
That opened the floodgates, with Willian adding a second 17 minutes later, Dudu scoring a spectacular third from 25 metres out and substitute Deyverson heading home the fourth nine minutes from time.
Palmeiras, who are led by former Brazil and Chelsea manager Luiz Felipe Scolari, are now unbeaten in 21 league games.
They can secure the title on Sunday at Vasco da Gama. Flamengo visit Cruzeiro the same day.
(Reporting by Andrew Downie, editing by Nick Mulvenney)
