The conversion from the latter gave the home side a 12-10 lead inside the opening half hour.
Richards took back the initiative with his 10th try of the Super League XV campaign but his poor form with the boot, missing his first three conversion attempts, denied the visitors a commanding early lead.
Roberts was forced to drop into the full-back role for Wigan after Phelps went off injured but the Australian appeared to relish the challenge as he scored twice and set up Tomkins's second.
Chase was sin-binned for punching on 64 minutes but Castleford hit back despite being a man down, as Michael Wainwright's darting run took him into the left corner.
Roberts found himself on the end of simple carry over for his hat-trick before Michael Cooper added a late consolation which was converted by Westerman.
Wigan coach Michael Maguire:
"I'm pleased for the boys. It was always going to be a difficult assignment coming here and Cas definitely made it a tough battle for us.
"I knew Amos [Roberts] from back in Australia. He's got that X-factor about him.
"He came up with some individual brilliance. I got him to work hard in pre-season and he's been playing outstandingly well for us."
Tigers coach Terry Matterson:
"I'm not too downhearted. I thought we gave a good account of ourselves. The scoreline was a bit harsh. If you score 22 points, it should be enough for us to win the game.
"We came up with some bad decisions at times. We had to play at the top of our game today to get the result. We were near to that in the first half but we weren't quite on it in the second half."
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