The former manager was also full of praise for Theo Walcott after another fine display from the striker.
After a disappointing midweek loss to Olympiacos in the Champions League, the pressure was firmly on the Gunners for their big clash with United on Sunday.
Arsenal answered their critics resoundingly, though, with three goals inside 30 minutes putting them into a commanding lead that Louis van Gaal’s side failed to respond to.
It was an impressive performance from Arsene Wenger’s side, who at their very best throughout the game, and Souness was full of praise for the display they put on at the Emirates.
“They were fabulous today,” he said Sky Sports 1 on Sunday evening (October 4). “If you’re a big club, looking to win the league, you’ve got to be bang at it from the first minute.
"Arsenal turn up sometimes and just play pretty football, today they were so effective against Manchester United because they put them under so much pressure.”
Walcott display the best Souness has ever seen
After being the star of the show in the win over Leicester City recently, Alexis Sanchez was once again on fine form as he scored two of Arsenal’s three goals of the afternoon.
The Chilean will grab the headlines given the quality of both goals, but it was another of his teammates who deserved praise for his effort throughout the game.
Theo Walcott again started up front for the side, with his constant running and pressure a danger to the United defence throughout. And Souness says the display was the best he has ever seen the striker.
“Theo Walcott, I think that’s the best I’ve ever seen him play,” he added. “With his runs off the balls, he was a threat throughout. His performance today was the best I’ve ever seen him play.”