Having already shocked Chelsea and Arsenal this month, the former England boss added a third major result as Christian Benteke’s brace secured a 2-1 win which dents Jurgen Klopp’s Champions League hopes.
Philippe Coutinho gave the Reds the lead with a sumptuous free-kick in the 24th minute but Benteke once again haunted his former club, finishing a swift counter-attack from close-range then nodding home a second-half corner.
The Belgian has now scored seven times in eight appearances against the Reds, a ratio that sits in stark contrast to his record as a Liverpool player.
Premier League survival is not yet a mathematical certainty but few now would disagree that Allardyce’s primary mission at Palace is complete.
Basking in the result, Allardyce was quickly on the front foot as he explained it.
“I thought we were, from start to finish today, tactically exceptional,” he said.
“With our limited possession we exposed Liverpool’s weaknesses time and time again today and ultimately that has brought us from 1-0 down to win it.
“I give the players a huge amount of credit for the way they defended and how they exposed the weaknesses of Liverpool defensively, which in the end they couldn’t cope with.”
The 62-year-old was happy to expand on his assessment, which focused on Klopp’s isolated centre-backs, though at this stage of the campaign Liverpool’s defensive frailties — particularly at the set-piece — are widely known.
“Liverpool at home play a superb attacking style in terms of football which means that both full-backs will go right up the pitch. It is very similar to Arsenal which means (Joel) Matip and (Dejan) Lovren are very exposed,” he said.
“Because they are very exposed in that position, if you get the right runners in behind then they are two big men that don’t like turning and going back to goal.
“On the corners everyone knows Liverpool are pretty weak, they conceded six off corners which we told the lads about. It’s now seven off that corner that has got us the winner.”
Benteke admitted he felt eager to impress when facing his former employers.
“I was motivated, I would say,” Benteke said.
“We knew it was going to be hard to play against them, but I give all the praise to the lads for the hard work.”
Benteke did not celebrate either goal too much, but marked his first of the afternoon with an elaborate handshake with Mamadou Sakho, the Liverpool defender who is on loan at Palace and who was watching from the bench.
“I said to myself if I got a chance to score I want to celebrate because I respect Liverpool but what happened when I was here is behind me and I was really looking forward to helping my team-mates,” he said.
Liverpool manager Jurgen Klopp had spoken of the threat Benteke posed if they allowed Palace to provide service to him and he was not happy the visitors had such an easy time achieving the feat.
“Christian Benteke is an outstandingly good striker, absolutely no doubt about it,” said the German, who sold the forward in the summer.
“But if you leave him alone like we did for the first goal I am not sure he needed all his skills for this goal. It makes no sense to leave him alone.
“For the second goal just one player reacted and that is our mistake.”
Klopp insists they have not blown their Champions League chances despite opening the door for Manchester United and Arsenal, both with games in hand, to catch them in the race for the top four.
“I know there are a lot of people around thinking ‘Oh my God, Champions League slips through our fingers again’ but only if we let it slip,” he added.
“We have to try everything and we will try everything. Our job is to squeeze everything out of the season we can squeeze.
“Obviously it is not easy for us, that is not a surprise.”
Mignolet, Clyne (Grujic 84), Matip, Lovren (Alexander-Arnold 79), Milner (Moreno 82), Can, Lucas, Wijnaldum, Firmino, Origi, Coutinho.
Hennessey, Ward, Kelly, Tomkins, Schlupp, Milivojevic, Zaha (Van Aanholt 78), Cabaye (Delaney 83), Puncheon, Townsend, Christian Benteke (Campbell 88).