Liverpool fought back to earn a potentially vital Champions League point with a 1-1 draw against Spartak Moscow in Russia.
Loris Karius was beaten all too easily in the Liverpool goal by a Fernando free-kick after 23 minutes, but the Liverpool goalkeeper's blushes were spared as Coutinho hit back for the Reds soon after.
Coutinho - a summer transfer target for Barcelona - finished a well-worked team move with a fierce drive eight minutes later to level the scores.
Liverpool had chances to win the game late on as Mohamed Salah was superbly denied in the 96th minute, but the result keeps Liverpool in contention after two back-to-back draws in Group E.
Coutinho, Mane, Salah and Roberto Firmino started for the first time together, but there were more misses than hits for Klopp's much-feted attacking quartet as a second successive draw in the competition made it just three wins in the last 14 group matches for Liverpool. The outcome handed the advantage to Sevilla, who lead Group E by two points after their win over Maribor.
The only other time the Reds boss fielded that quartet was in the 3-0 pre-season Audi Cup win over Bayern Munich and, in fact, he named exactly the same 11 players from that game to do the job at the Otkrytiye Arena.
It was an easy selection which no-one could criticise Klopp for. His decision to rotate his goalkeepers, however, could be one which comes back to haunt him.
Karius is the man preferred for the Champions League and he spoke pre-match about proving to the manager he was ready for a full-time role.
He still has some convincing to do after seemingly being slow to react as Fernando curled home a 25-yard 22nd-minute free-kick, continuing a Champions League theme for Liverpool of conceding their first shot on target.
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But it was the loss of possession on halfway by Emre Can, booked earlier after being let down by poor control, in the build-up to Coutinho's foul which left the right side of defence exposed. Germany midfielder Can was the most culpable of anyone.
Mane was flagged offside as he stooped to head in Trent Alexander-Arnold's wicked cross before two of Klopp's 'Fab Four' produced the equaliser.
Coutinho exchanged passes with Mane to burst through and clip an angled shot past Artem Rebrov - the 200th goal of Klopp's 110-game reign.
Liverpool should have taken the lead just before half-time as they broke from a Spartak corner to have a four-on-two attack, only for Mane to stray offside from Jordan Henderson's low cross.
Early in the second half a low Coutinho free-kick was well saved, with Salah unsuccessfully appealing for a penalty for a push in the back, forcing him to collide with Rebrov which eventually forced the goalkeeper off injured.
Daniel Sturridge and Georginio Wijnaldum were sent on in the last 20 minutes to inject life into a flagging performance, with the former stabbing wide and then volleying over - both from close range - in the closing stages.
Moments from the final whistle, Salah had a point-blank header saved by substitute goalkeeper Aleksandr Selikhov.
Additional reporting by the Press Association.