One week on from thumping the Czech champions 5-1 in the first leg of their last-16 tie, the Reds bettered their previous tally with a 6-1 second-leg thumping at Anfield, soaring into the quarter-finals 11-2 on aggregate.
Four of Liverpool's goals arrived during the first 14 minutes of the match, where Clark opened his senior Reds account with a crisp low strike after Mohamed Salah intercepted a loose pass from Ladislav Krejci.
The 2005-born protege subsequently turned provider for a record-breaking Salah goal thanks to another defensive howler from Sparta, who also conceded to Darwin Nunez and Cody Gakpo in that 14-minute annihilation.
Veljko Birmancevic got the visitors on the board on the stroke of half time, but Gakpo's second and a deflected Dominik Szoboszlai strike in the second half capped off an emphatic Liverpool triumph, albeit one that was slightly marred by Clark's withdrawal.
Klopp had intended to bring Salah off for 20-year-old debutant Mateusz Musialowski for his final substitution, but Clark appeared to have hurt his ankle and was withdrawn instead, thus forcing Salah to complete an unplanned 90 minutes.
Speaking to TNT Sports, Klopp confirmed that the Egyptian had come through unscathed, and while he is concerned about Clark's issue, he is keeping his fingers crossed that the teenager has avoided something serious.
"He played incredibly. It was his first goal but he won the ball back after another one. He is the one I am worried a bit about, we wanted to take off Mo [Salah], but Bobby sits on the ground and says he feels something in the ankle," Klopp said.
"He felt something, but it was intense for the boy, he was running around like crazy. Let's hope that's nothing. The steps the boy made though, pfff [wow]. We've had such a difficult situation with all the injuries and then the boys stepped in and took their chances. So very happy with that, they were exceptional again."
While Clark gingerly trudged off the field, Salah looked in good nick on his first start for the Reds since New Year's Day, as he became the first-ever Liverpool player to score at least 20 goals in all competitions seven seasons running.
The 31-year-old also registered three assists for Clark, Gakpo and Szoboszlai, and Klopp had no doubts about the winger's ability to dig in and see out the five-goal triumph, even if he did have to ask him to stop tracking back.
"Mo is a very experienced player, I told him if he has to stay on then he may have to play the full game. He did and it was the first time I told someone to stop defending," Klopp added.
"He actually then nearly made another goal but Cody was offside. He's very experienced so he got easily over the line. All fine, all good. We wanted to go through, we wanted to play well and score goals and we did that."
Atalanta BC, Marseille, AC Milan, Roma, Bayer Leverkusen, West Ham United and Benfica will be Liverpool's potential opponents in the quarter-final draw, which takes place at 12pm on Friday.
The Reds, who are still on for a quadruple in Klopp's farewell season, are next in action on Sunday, facing Manchester United at Old Trafford in the quarter-finals of the FA Cup.