Richards opened the scoring in the 11th minute when a 50-50 challenge between Paul Linwood and Paul Edwards ended with the ball breaking to Ross Davidson. He slid a pass to the striker who had time to pick his spot and give his side the lead.
Chester nearly drew level just before the interval when a deflected shot from Ryan Lowe was about to creep over the line until it was hooked away by Sam Stockley. Lowe and debutant Eddie Johnson also shot wide as Chester came strong in the closing stages of the half.
The home side should have equalised within 30 seconds of the restart when Lowe's 20-yard shot struck the post and the rebound fell to Johnson, but the striker ballooned his shot well over.
Lowe had a 'goal' ruled out for offside in the 57th minute when the striker followed the ball in after keeper Joe Anyon had saved Johnson's initial shot.
Louis Dodds then had a chance to finish the game off after being fed by Richards but he pulled his effort wide of the post.
Vale looked as though they had made the game safe when substitute Richman finally bundled the ball home in the 78th minute after Richards and Dodds had both seen their efforts cleared off the line in a mad goalmouth scramble.
But Chester ensured an anxious last few minutes for the visitors when they pulled a goal back five minutes from time following a brilliant run by substitute Paul Taylor.
He waltzed past several defenders before setting up Lowe, who side-footed the ball home, but it proved to be too little too late for City.