Adam Milner was denied a try for the home side within the first minute of the match when the referee ruled that he had not crossed the line.
The day's first try eventually came on 14 minutes, when Warrington veteran Lee Briers's wonderful run took him through the heart of the home defence.
Castleford continued to play some magnificent rugby, though, and took the lead through Justin Carney after a wonderful flowing move.
The home team refused to be beaten, and Craig Huby gave them something to cheer when he levelled the scores at 30-30 just past the hour mark.
With the game approaching a frenetic finale, quickfire tries from Higham and Joel Monaghan ensured that the visitors left with a win.