The hosts drew first blood with a penalty after Kirkby were penalised for not releasing in the tackle.
The second in the table visitors had the lion’s share of territory however and Dave Barton’s brilliant chip and chase saw him score under the posts with Tom Pickthall converting for a 7-3 lead.
Another penalty saw Warrington reduce the arrears to one point but Kirkby hit back with captain Ben Walker scoring a fine individual try as he outpaced the cover to touch down after a hack down field.
Turning round 12-6 to the good Kirkby were looking to build towards victory but Warrington struck first with Zak Lythgoe touching down meaning the lead was again just one.
Lythgoe then clashed with Kirkby’s David Cooper-Dunne as both were sent to the sin bin with the extra space playing into the visitors’ hands as David Bird scored in the corner to once again keep Warrington at bay.
The hosts kept coming however and after hammering the Kirkby line they crossed for an unconverted score with 10 minutes to play to make it 17-16.
Warrington, who had trailed since the early stages, then went in front with three minutes to play, as a kick was gathered and they crossed in the corner to make it 21-17.
The back and forth game had one final act however, Barton crossing for the winning try that also saw Kirkby pick up a bonus point.