The Republic of Ireland international made his first start of the season at Anfield on account of Alisson Becker's muscle injury, which he aggravated during the midweek Champions League win over AC Milan.
Kelleher's maiden appearance of 2024-25 came just a couple of weeks after he lifted the lid on his summer frustrations, admitting that he was desperate to go and be a number one after years as Alisson's backup.
Liverpool are believed to have rejected a late bid from Nottingham Forest for Kelleher, whom they slapped a £25m price tag on, and no parties met the Reds' valuation before the window shut.
The shot-stopper could have perhaps expected a quiet afternoon against the Cherries, although he had to make a couple of crucial of second-half interventions to preserve Liverpool's clean sheet, firstly making a strong one-handed save from Luis Sinisterra.
Slot: 'Liverpool needed Kelleher in Bournemouth win'
From a following corner, the ball deflected off Sinisterra's shoulder and hit the crossbar before bouncing off the thigh of Trent Alexander-Arnold, who needed Kelleher to rapidly claw the ball off the line to prevent a late own goal.
In his post-game press conference, Slot told reporters that it was a "good thing" that Liverpool had Kelleher in between the posts today after the board priced the Irishman out of a desired exit over the summer.
Asked about the importance of having two top-quality goalkeepers in the squad, the Dutchman replied: "Yeah, but not only two goalkeepers, also two good wingers, left wingers, two good right wingers, two good strikers. That's what you saw today.
"I just said about Cody [Gakpo], how good he was in San Siro, how good Lucho was now - and it's the same with the goalkeepers. We needed our goalkeeper today more than in all the other matches we played before because, like I just said, Bournemouth got more chances than I am used to seeing the other teams getting against us in the first six games of the season.
"But it was a good thing that we had Caoimhin today because he made some really good saves - which Alisson [Becker] did in the other games as well, but he didn't have to make that many as Caoimhin made today."
Slot questioned Darwin Nunez shot choice before terrific goal
Before Kelleher was seriously called into action, Liverpool capitalised on atrocious Bournemouth defending in the first half, as Luis Diaz notched a brace before Darwin Nunez curled in a brilliant third into the bottom corner.
The Uruguayan was making his first start of the season against Andoni Iraola's side and repaid Slot's faith in him, although the Liverpool boss admits that he believed Nunez shooting to be the wrong choice before his effort found the far corner.
"My first instinct when he shot, I said, 'Why does he shoot? Why don't you keep on dribbling?' Because he made the ball free and I think the defender was on the ground," Slot added.
"But then there was a fraction of a second later when I saw the ball went in off the post and I was like, 'OK, maybe you are a better football player than I was in the past!' [A] good choice of him."
Liverpool's three-goal success has temporarily lifted them above Manchester City into top spot in the Premier League table, and the Reds return to action at home to West Ham United in the EFL Cup third round on Wednesday.