Wakefield lost their place in the top four at the end of the regular season before losing to Huddersfield last weekend.
Their poor start to the Super 8s had raised eyebrows but Chester's men responded brilliantly on Thursday night.
Half-back Jacob Miller was in inspired form on his return from a broken leg and he helped Wakey record their biggest ever Super League win over their Yorkshire rivals.
Wakey returned to the top four with the victory and Chester insists they can stay there.
He told reporters: "We've copped some criticism over the last seven days and rightly so because the performance last week wasn't to the standards we've set ourselves.
"But we answered a few questions tonight. We scored some nice, fancy tries but the defence was the best I've seen it in a long time. We copped a bit but we're now in that top four. Who'd have said that at the start of the year?
"We've shown with this performance tonight we're not here to make the numbers up.
"We've got as good a chance as anybody competing for the top four. We need to take a lot of confidence from that result."