The Goodison Park club were in deep trouble just weeks ago, with their position worsened by the docking of eight points for financial breaches.
But they have turned the corner in dramatic style this month, winning four out of their past five matches, with the outlier a 6-0 defeat by Chelsea at Stamford Bridge.
Everton midfielder Idrissa Gueye delivered the decisive blow against Brentford, driving home in the 60th minute.
The win took Dyche's men to 36 points -- 11 clear of Luton, who are 18th in the table and have just three games to play.
It is a huge relief for the nine-time English champions, who have been ever-present in the top-flight since the 1954/55 season.
"Incredibly pleased and proud," said Dyche, who also faced a tough battle last season to keep Everton up after being appointed in January 2023.
"They're a group of players who have had knocks all season. Four out of five clean sheets and wins with all the mounting noise after the Chelsea game is incredible.
"The mentality of the players is fantastic. Super pleased. Very proud."
The former Burnley boss said it had been an "exhausting week", which included a rare 2-0 home win against Merseyside rivals Liverpool.
"The emotion that goes into that, I wondered how the players would respond," he said.
"With XG (expected goals) we've been questioned for how many times we haven't won games. It's paid us back.
"They've had a massive week. There's a lot of pressure and intensity on the week and can you do it again? Second half we controlled the game pretty well."
