Jürgen Klopp made nine changes to the side that beat Sheffield United in the Premier League a few days earlier, but his fresh-faced team delivered at Anfield when Jones fired in a wonderful 71st-minute strike off the crossbar.
Here are five talking points from the 235th Merseyside derby....
Shooting starlet
Jones' celebrations were all over the back pages of the UK press after he arced a 20-yard shot over Everton goalkeeper Jordan Pickford to secure victory on Sunday.
"It's massive," said the man himself after the strike made him Liverpool's youngest goalscorer (18 years, 340 days) in a Merseyside derby since Robbie Fowler in March 1994.
Handed his second senior start of the season, Jones, who has scored 13 goals in the youth ranks this term, played through illness to leave his indelible mark on Anfield.
And it wasn't just his sensational strike that was worthy of note. The confident forward's all-round display was impressive as he led the side with a 96.4 per cent pass completion rate in the opposition's half and set up three key chances for his teammates.
Safe hands
At the other end of the pitch, Liverpool goalkeeper Adrian made three crucial saves to deny Everton early in proceedings as he came in to deputise for Alisson Becker.
The 33-year-old Spaniard, who joined the Reds in August, is already something of a cult figure following his penalty shootout heroics in the UEFA Super Cup final and he made some fine stops to delight the fans here.
His save from Mason Holgate's close-range header was probably the pick of the crop and kept Liverpool in the game during the opening stages of the derby, when Everton enjoyed a flurry of attacks.
Liverpool went on to control the match after Adrian helped lay the foundation upon which to build. He secured the Reds' fifth consecutive clean sheet in the process.
Minamino watch
The home fans were granted a first glimpse of new signing Takumi Minamino as Klopp handed the Japan international a 70-minute runout against Everton.
Able to play anywhere across the front three - as the manager noted in his pre-match comments - the LFC No.18 was deployed at the tip of the Reds' attack on his Anfield bow.
Minamino average position and heatmap
Supported by Divock Origi and Harvey Elliott on the flanks, Minamino had 33 touches and enjoyed an 86.4 per cent pass completion rate as he made a promising start to his Liverpool career.
Often used in one of the wide attacking positions for former club Salzburg, he scored 64 goals and provided 44 assists in 199 games for the Austrian side.
Debutants and depth
Minamino wasn't the only player to make his debut on Sunday, with Liverpool youngsters Nathaniel Phillips and Yasser Larouci also making their competitive bows.
Centre-back Phillips, who has recently returned from an 11-game loan spell at 2.Bundesliga side Stuttgart, started the match, while Larouci came off the bench to replace the injured James Milner after just nine minutes.
With the likes of 18-year-old right-back Neco Williams and 16-year-old winger Elliott also impressing in the side, it would appear Klopp has plenty of talented youngsters to call upon if required.
Derby-day don
The boss made a little bit of history on Sunday, too, as he equalled the unbeaten derby day streak of legendary Liverpool manager Bob Paisley.
Klopp is unbeaten in all 10 of his clashes with Everton since taking charge of the Reds in October 2015, winning seven of them and drawing three.
That matches Paisley's club record of most derbies undefeated from the start of a managerial career.
Klopp's men are also the first Liverpool side to beat the Toffees twice at Anfield in the same season since the 1986-87 campaign.