Manchester City's late winner against Wolves saw the Reds briefly knocked off top spot as they prepared to play host to Enzo Maresca's in-form Blues.
The hosts responded emphatically, with Jones winning a first-half penalty following a challenge from Levi Colwill that was duly converted by Mohamed Salah.
Jones remained integral to Liverpool's control of the game throughout, and restored their advantage with a close-range finish just minutes after Nicolas Jackson had drawn Chelsea level in the second-half.
After netting his first Premier League goal of the season, the Liverpool academy graduate dedicated his strike to his newborn daughter as he celebrated in front of a delighted Anfield crowd.
Jamie Carragher heaped praise on Jones following the game, calling the midfielder 'brilliant'
Speaking following the game, Jamie Carragher insisted Jones could soon cement a place in Arne Slot's starting XI if he can maintain his momentum going forward.
'Jones was brilliant, he was outstanding,' Carragher said on Sky Sports. 'He still hasn't really made himself first choice but what a performance.
'He's got to keep playing like that. He's up against two top players in there. I keep thinking will Slot go back in for [Martin] Zubimendi, when you see performances like that I'm thinking no.'
With Alexis Mac Allister, Dominik Szoboszlai and Ryan Gravenberch impressing in midfield in Slot's debut campaign on Merseyside, Jones has found Premier League minutes hard to come by.
Liverpool's 1-0 win over Crystal Palace before the international break marked his first league start of the season.
But with Mac Allister still struggling with an injury picked up during the clash at Selhurst Park, Jones was given his opportunity to shine in midfield.
Tasked with stifling his former England U-21 team-mate Cole Palmer, Jones excelled for the Reds on Sunday and was subsequently named the man of the match.
'Curtis Jones was very good.' Slot said after the game.
'The team worked very hard. Curtis had a difficult job - he had to keep Palmer quiet. He added some very important moments. He was in both parts of the pitch very important.'
After one of his most effective displays since making his senior debut for the club just days after becoming a father for the first time, Jones offered some insight into how prepared for such a crucial game amid hectic circumstances.
He said: 'I've been a Dad a week, it's the best thing ever, i'm playing with a smile on my face it's a different type of joy.
'My little girl will be proud as well so i hope my girlfriend and baby are at home with a smile on her face. I was in the spare room but she's a little dream. I just thought it's wise I stayed in the spare room.'