The Gunners made the most of Liverpool dropping points and drawing at Newcastle by following up their 5-2 victory over West Ham on Saturday with victory over their old foes.
Set piece specialists Arsenal were in full flow under the lights at the Emirates Stadium.
First, Jurrien Timber scored the home side's opener with a header just after half time from a corner.
Their second goal also came from a corner, with Thomas Partey heading a cross back across the box for William Saliba to turn in with his backside.
And Neville, who played in Man United's defence for his entire career, was furious with his former side's marking.
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Speaking on the Overlap live stream watchalong of the game after Saliba's goal, he said: "That's s*** that."
Partey was completely unmarked at the far post, while Saliba shook any pressure from the Red Devils present in the box with ease.
"Your set pieces are a joke," Neville later moaned to co-pundit Ian Wright.
"I have a lot of admiration for it," he added.
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Arsenal have scored more goals from corners than any other side in the Premier League since the start of last season (22).
Meanwhile, the two players with the most assists from set plays in this time are Declan Rice and Bukayo Saka with seven each.
Last season, the Gunners levelled the record for most Premier League goals scored from a corner.
They drew themselves level with West Brom and Oldham's 16 goals from the set piece in 2016/17 and 1992/93 respectively.
Arsenal have now won their last four league games against Man United.
They've made history in the process, having never won four in a row against them in Premier League history previously.
The Gunners have won the last four league clashes against the Red Devils 3-2, 3-1, 1-0, and now 2-0.
Arsenal are now third, seven points off leaders Liverpool.
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Chelsea are in second with the same points as the Gunners but with superior goal difference after their 5-1 win over Southampton.
Man United, meanwhile, sit in 11th as Ruben Amorim's unbeaten start to life as Red Devils manager came to an end.