Both teams started brightly with an attacking onus shown by Bournemouth and Liverpool. Despite the intention to score, very few clear chances were created in the opening 30 minutes despite Liverpool scoring to open their lead.
Harvey Elliott latched onto a ball outside the box before striking it which deflected off of Cody Gakpo and forced the goalkeeper to make a reaction save but the ball fell right in front of the Dutchman who scored his second goal of the competition.
Liverpool almost doubled their lead a few minutes later as Dominik Szoboszlai found space on the edge of Bournemouth's box but his shot went narrowly wide.
It was very nearly 1-1 after just minutes in the second half as Joe Gomez cleared Alex Scott's looping corner off the line as he saved Kelleher's blushes who was beaten.
Antoine Semenyo was one-on-one with the Republic of Ireland international after being put on goal thanks to a pass by Kluivert but he could only put it wide.
It wasn't long before Bournemouth converted one of their chances as in the 64th minute, another dangerous corner from Scott was met by Kluivert who headed in from close range to level the score-line.
With Darwin Núñez, Alexis Mac Allister and Trent Alexander-Arnold on for Liverpool, the side's vice-captain played a long ball to Nùñez but the striker controlled the ball poorly but still managed to score an absolute stunner after curling the ball past Radu from outside the box.
Both sides had chances on the counter but Liverpool failed to increase their lead while Bournemouth weren't able to find a second equaliser as they crashed out of the EFL Cup.
LFC Globe Verdict
Liverpool struggled at times against Bournemouth who played their strongest team but had enough quality to get the all-important win to move on to the quarter-final of the domestic competition.
Man Of The Match And What's Next?
Jarell Quansah continues to impress Liverpool fans across the globe with his performances despite his tender age of 20 years old.
Making his debut this season, Quansah consistently goes from strength to strength every time he plays as Klopp has uncovered yet another gem from Liverpool's academy.
Liverpool have now won four games in a row in all competitions and are back in action on Sunday as they travel to Kenilworth Road to take on Luton Town on November 5th at 16:30PM (UK time).