The Italian, on loan from champions-elect Liverpool, kept his cool to carefully slide home a second-half penalty on Saturday and inflict manager Jose Mourinho's first Premier League home defeat at the 78th attempt.
The penalty also handed a major boost to parent club Liverpool's chances of winning the title for the first time in 24 years.
"I like to make history," Borini told reporters at Stamford Bridge. "This season has been fantastic for me and I achieved a few things that will always be in the history of Sunderland, like this game.
"It is a great target when you come here and you play against a team that never gets beaten at home and you have the chance to be the first."
Borini made 13 league appearances for Liverpool last season after signing from AS Roma and had a spell at Chelsea under Mourinho earlier in his career.
The 23-year-old striker, who also played for a short time under Liverpool manager Brendan Rodgers when he was in charge of Swansea City, said he expected to go back to Anfield at the end of the season.
"My first thoughts are on Sunderland, that's the shirt I'm wearing," said Borini who shared a warm handshake with Mourinho at the start of the second half.
"Obviously I watch the Liverpool games and I'm happy if they win and play well but my first thoughts are with Sunderland.
"I need to think about myself, the past is the past. There was a chance to take the penalty, I took the last two penalties and I took this one."
Sunderland are three points from safety with four games to go but also recorded a surprise result during the week when they went to Manchester City and held the league's third-placed team to a 2-2 draw.
With fellow strugglers Cardiff City the visitors to the Stadium of Light next Sunday, Borini has urged his team mates to continue their fine run of form against Ole Gunnar Solskjaer's side.
"We got out of two difficult games with four points and nobody expected us to win any," he added. "Against Man City we could have gone away with three points - that was probably the turning point.
"Cardiff is a bigger game than this one against Chelsea because now it's all about winning games and we believe we can do it."
(Additional reporting and editing by Tony Jimenez) nL3N0NC07B
