Arsene Wenger's career is notable for his loyalty to the players who deliver for him, and that devotion tends to endure regardless of opponent, occasion and sometimes in spite of the form, which all made the absence of Alexis Sanchez that more unusual.
Arsenal's best player sat out the first half at Anfield only to be called upon to try to lead a comeback after Wenger's team reached half-time 2-0 behind and in danger of being blown away. The Arsenal manager will believe, as ever, that he has the experience and authority to make the big calls but this decision only ramped up the for a man who is already under the usual late-season pressure, his decision seemed only to make that more intense.
This was the meeting of the top six's two problem clubs, both of them in danger of losing the thread of their seasons and in need of victory. It was Jurgen Klopp's team who seized the initiative and, after Danny Welbeck's second-half reply, scored a third in injury-time through Georginio Wijnaldum. On the touchline Klopp hugged a supporter while on the Arsenal bench Wenger sunk lower into his coat.
A bleak day for the Arsenal manager but as ever the big picture is different: his team can reclaim fourth place from Liverpool if they win their game in hand. Where this leaves them in terms of mood and momentum when it comes to Tuesday's game against Bayern Munich at the Emirates, with a 5-1 deficit to make up, will be another matter.
They have lost four of their last six in all competitions. There were some critical moments at the end of the first half for Arsenal when a third goal for Liverpool would have made any comeback impossible and the booing that rang out from the away fans at the half-time whistle that much louder and meaningful.
As for Klopp, this was the performance he had been looking for after defeat to Leicester on Monday, and really it should have been over by half-time. His team struck through Roberto Firmino and then Sadio Mane in the first half and were the dominant side before the break.
Instead of rising to the occasion, Wenger's alternative line-up, without Mesut Ozil who was ill, faltered badly. The front four of Alex Oxlade-Chamberlain, Alex Iwobi, Welbeck and Olivier Giroud barely managed to scrape together a chance before the break, and if this was Arsenal being direct then it was hard to see the difference. They lacked the individual quality that the likes of Sadio Mane, scorer of the second goal, and Coutinho contributed at the other end.
That was not to overlook Adam Lallana who played a key role in the first goal and whose energy drove Liverpool forward into the key positions from which they scored. They might have had more with two chances for Coutinho in the final minutes of the half when Arsenal were barely hanging on and Klopp urged his players forward in the closing minutes of the half to try to kill the game.
In midfield, Francis Coquelin and Granit Xhaka were over-run in the first half with the former booked for desperately clutching at Lallana's shirt as the Englishman accelerated away from him.
The first goal was a surging attack in which Liverpool managed to get numbers forward and Lallana switched the ball right to Mane. His cross went through the legs of Coutinho and reached Roberto Firmino at the back post, where he could afford to take a touch to steady himself before dispatching it past Cech.
Even before the second goal there was a moment when Coquelin found himself robbed of the ball with relative ease by Mane, who gets away from the scene so quickly. He finished beautifully on 40 minutes when the ball came to him via Milner, Wijnaldum and then finally Firmino to the right side of the area.
The change was not quite instantaneous when Sanchez came on at the break but the mood was lifted for Arsenal, who came close to a goal within three minutes of the half when Giroud's header was pushed upwards by Simon Mignolet onto the top of the bar, from where it dropped down back into play.
Even so it was Liverpool who pushed for the third goal which would decide the game and it was while they were doing so that they allowed Arsenal back into it.
The ball was won in the right-back position and, with Liverpool committed to the attack, was moved quickly to Sanchez, where he surged forward. The ball was played inside right-back Nathaniel Clyne but it was well wide of the goal and still asked a great deal of Welbeck, who ran onto it and finished with a lovely chip over Mignolet.
It was a brilliantly taken goal, Welbeck's first in the league since April and a reminder of Liverpool's vulnerability on the counter-attack.
Wenger sent on Lucas Perez and Theo Walcott in search of the equaliser and the latter did well to leap over the converging challenges of Joel Matip and Emre Can, who collided heavily and left the latter limping.
Divock Origi replaced Coutinho and his header struck Cech's left post but eventually the breakthrough came. It was Lallana's fine ball to Origi who crossed for Wijnaldum to seal victory.