Poyet replaced Paolo Di Canio as head coach in October when Sunderland were bottom of the table with only one point from their first five top-flight games.
The Uruguayan stated after a 5-1 hammering at Tottenham last month that it would take a "miracle" for the Wearside club to avoid relegation, but they are safe with a game to spare after beating West Brom 2-0 on Wednesday.
Sunderland also reached the League Cup final, in which they were beaten by Manchester City, and on-loan striker Borini believes Poyet should take great credit for the impact he has made at the Stadium of Light.
"He (Poyet) has had a great impact," Borini told Sky Sports News. "He changed our style of play, and we built up confidence by playing the way he wants us to play.
"That made all the difference, especially at the end of the season when probably everyone thought we were dead.
"We showed that with good football, solid and compact we can achieve good results."
Italian striker Borini has scored nine goals in 39 appearances in all competitions this season.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
