The Reds have cruised to the title - their first in 30 years - but showed signs of a hangover from Wednesday's trophy celebrations as they trailed to Dwight Gayle's first-minute opener.
Virgil van Dijk equalized and Divock Origi then grabbed his first goal since December before Sadio Mane added late gloss to the scoreline as Liverpool finished the campaign with 99 points, their best ever top-flight haul and only one shy of Manchester City's 2017-18 record.
The surprise Gayle goal had seen Newcastle lead Liverpool early for the second time this season, with this 25-second effort the fastest the Reds have ever conceded in the Premier League.
Allan Saint-Maximin quickly won a foul on halfway and Jonjo Shelvey's free-kick sent Gayle clear to stab past Alisson, prompting a lengthy VAR review for a potential offside before the goal was given.
Liverpool's subsequent dominance initially spawned only a speculative Takumi Minamino effort, which Martin Dubravka saved well, before Alisson had to be alert to field an unorthodox Federico Fernandez drive at the other end.
But with the Reds' usual attacking stars watching on, Van Dijk stepped up and looped a towering header over Dubravka from Alex Oxlade-Chamberlain's right-wing cross.
Klopp readied Salah, Mane and Firmino as Liverpool made a slow start to the second half, yet the imminent changes provoked Origi to blast in the visitors' second, his shot passing through a crowd of bodies to deceive Dubravka and pick out the bottom-right corner.
The triple substitution followed regardless and Salah's first involvement saw a powerful strike bounce off the post, but it was Mane who provided the final flourish.
Cutting inside from the left in trademark fashion, the winger curled beyond Dubravka to end Liverpool's season in style.
What does it mean? Record-breaking campaign ends in fitting fashion
There has been plenty of attention given to the landmarks Liverpool have not matched this season, losing their unbeaten record to Watford and then slowing after the restart to miss out on the opportunity to earn 100 points.
But few Reds fans will be complaining as they reflect on the campaign and this latest record - besting their 97 points last season and 98 in 1978-79 (when adjusted to three for a win) - provided an apt finale.
Back-up Origi ends goal drought
For close to an hour, Klopp's makeshift XI displayed the few shortcomings in this Liverpool squad. Without their star attacking trio, the champions rarely tested Dubravka.
Oxlade-Chamberlain was industrious, while Minamino is still finding his feet, but it fell to Origi - scoring just his sixth goal of the season - to really make a mark.
Early error provides scare
There have been a few too many defensive Liverpool mistakes since the title was wrapped up - including in the midweek 5-3 win over Chelsea. The latest saw Joe Gomez caught out of position as Gayle ran through.
Klopp will hope such lapses do not linger into next season.
Neither side have FA Cup or European duties still to fulfil, meaning they can instead now look towards next season, with the Premier League returning on September 12.