Having inspired comebacks against Borussia Dortmund and Villarreal in recent weeks, the German achieved it again as one substitute Sheyi Ojo crossed for another to nod home in the second minute of added time.
Up to that point the visitors appeared set to register their third successive Anfield victory as a rejuvenated Eden Hazard scored his fourth goal in as many matches.
The Belgium international has some ground to recover ahead of Euro 2016 this summer after a disappointing season but has discovered his old spark again.
A month out injured with a hip problem seems to have had a restorative effect on the 25-year-old who had previously looked a shadow of the man who was last season's player of the year.
However, he was ultimately upstaged by his international team-mate who capitalised on goalkeeper Asmir Begovic only managing to palm Ojo's cross into the air.
It ensured Klopp's 50th match in charge - reaching the landmark in 217 days to comfortably beat the 254 it took both Bob Paisley and Joe Fagan - and the last at the ground before it undergoes a substantial facelift with a redeveloped Main Stand, did not end in disappointment.
It did not look that way as the seconds ticked down as after an early flurry of activity his side - barring injury the one he will select in the Europa League final against Sevilla in Basle next week - played like one with bigger things on their mind.
A Chelsea team missing striker Diego Costa (injured), captain John Terry (suspended) and goalkeeper Thibaut Courtois (ill) defended better and crucially had one player in Hazard who actually looked like he was up for a match of no significance.
Even victory in their final game at home to champions Leicester will not improve Chelsea's ninth-place position, but if Hazard is indeed back to his best next season he should be a different prospect providing, of course, he stays at Stamford Bridge for the arrival of new boss Antonio Conte.
The visitors weathered the early pressure with Baba Rahman blocking Phillippe Coutinho's shot, Begovic saving from Adam Lallana and Roberto Firmino firing into the side-netting after a heavy touch took him wide from Daniel Sturridge's excellent release pass.
Hazard gave Simon Mignolet one warning with a low shot which was parried before Kolo Toure cleared the danger but there was no second chance for the Belgium goalkeeper from his international team-mate in the 32nd minute.
Hazard skipped past Lallana, Firmino and Dejan Lovren - whose attempts at tackling had Europa League final written all over them - to bend a delicate shot inside the far post.
Bertrand Traore, in for Costa, curled a shot wide after Mignolet came for an over-hit pass and then retreated while, after the break, Hazard, Pedro and Traore tested Mignolet further.
Begovic's one task in the second half was to stick out a hand to brilliantly deny Sturridge one-on-one.
Further evidence, if any were required, of Hazard's renewed vigour came in the 80th minute when he burst into a sprint into his own penalty area to prevent Nathaniel Clyne crossing to substitute Benteke.
Klopp refused to give up on the result, however, and kept most of his big names - including Sturridge - on for the full 90 minutes in the knowledge few will play at West Brom on Sunday.
The last throw of the dice saw him replace centre-back Toure with Ojo and the young winger almost volleyed in the equaliser with his first touch but then crossed for the equaliser.