Andros Townsend, Yohan Cabaye and Luka Milivojevic found the net as Palace moved six points clear of the relegation zone whilst piling pressure on Allardyce’s old foe Arsene Wenger, who has lost his last four Premier League away games.
The commanding victory was no more than Palace merited for a robust and effective gameplan that saw Townsend and Wilfried Zaha feast off the service of target man Christian Benteke, who won eight aerial challenges against the meek Shkodran Mustafi and Gabriel.
Allardyce told Sky Sports: “The first thing was to defend correctly and as an 11 to frustrate Arsenal and keep them playing sideways and backwards.
“Then it was to use the ball and [move it] into the spaces behind the full-backs or up to Christian Benteke as quickly as we could.
“The weaknesses with Arsenal have been defensively. They leave Gabriel and Mustafi really exposed. Monreal and Bellerin play like right and left wingers. The wingers come inside with the centre-forward and they’re just left on their own.
“If you can get at them quickly through midfield and wide areas or off Christian [Benteke] you can get in the opposition’s box. You can get chances.
“Today with the workrate, the determination of the team to log on to Arsenal when they had the ball we won a lot of possession and created a lot of chances. Yohan Cabaye’s goal second half: what a finish. It was down to us shutting down throw-ins. That was the basis of us getting so many attacks off.
Allardyce added: “It wasn’t a shock tonight in terms of our performance. We played at Chelsea that way. The result is a shock for everybody but the performance was there at Chelsea.
“They did that and did it better.”