Christian Benteke's brilliant strike saw Liverpool beat Bordeaux 2-1 to qualify for the knockout stages of the Europa League with a match to spare.
The Belgium international's goal in first-half added time proved decisive after James Milner's earlier penalty had spared the blushes of goalkeeper Simon Mignolet, whose needlessly-conceded free-kick for time-wasting had allowed Henri Saivet to score.
In addition to his goal Benteke had a further two ruled out but ultimately his contribution was enough to send the Reds to Switzerland next month needing only a point against Sion to top Group B, although their place in the next round is already guaranteed after Rubin Kazan's win over the Swiss.
Benteke's brilliance in front of goal would have been welcomed by Klopp, especially as Daniel Sturridge's anticipated presence on the bench did not materialise after the striker was sent for a scan on his foot after complaining of discomfort in training.
In almost three years the 26-year-old has missed almost as many matches (68) as he has made appearances (70).
Benteke was brought in over the summer, at a considerable £32.5million cost, by former manager Brendan Rodgers who wanted a forward he could rely on for a whole season having suffered from Sturridge's injury problems for most of the previous campaign.
The Belgium international, who was left on the bench for Sunday's victory at Manchester City, has had his niggles since arriving but a fourth goal in his last nine appearances suggests he is more than capable of fulfilling the consistency requirement for his new boss.
Consistency is still an issue which dogs Mignolet, however, and that was all too evident on the night.
Just 13 minutes in he came out of his area to head the ball but directed it straight into the patch of Clement Chantome and only a block by Kolo Toure prevented the midfielder shooting into an empty goal.
Worse was to follow 20 minutes later when the Belgian goalkeeper's dithering, something which has been commonplace throughout his time at Anfield, proved costly.
Seemingly unable to find a team-mate to release the ball to he held on to it for 22 seconds - more than long enough for referee Alon Yefet to penalise him with an indirect free-kick, which was tapped to Saivet who drilled home.
Equally soft was the award of Liverpool's equaliser when the incredulous Ludovic Sane was adjudged to have fouled Benteke.
Even Klopp looked doubtful, pulling a face and turning to face the Main Stand so as not to watch as Milner converted from the spot - Liverpool's first penalty in 23 matches.
If that was generous Benteke's strike seconds before half-time was glorious, cushioning Nathaniel Clyne's pass out of his feet and instantly smashing a shot past Cedric Carrasso.
The goal allowed Liverpool to control the second half with Benteke, Milner and Jordon Ibe all going close but Mignolet was rarely troubled at the other end.