The Premier League leaders extended their advantage at the top to five points following goals from William Saliba and Jurrien Timber.
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Chelsea briefly equalised through a Piero Hincapie own goal but were reduced to ten men after Pedro Neto received a red card for a foul on Gabriel Martinelli.
“These are key games that you have to win and it doesn’t matter if you play good or bad and today was one of those games for Arsenal,” Vieira said after the game.
“I think the key moment in this season is going to be when Arsenal and Man City play, because after that fixture I don’t see either team losing.”