The Wire secured a 20-18 victory thanks to a late penalty at the Haliwell Jones Stadium.
Brown went close to atoning for his earlier error but was stopped from touching down between the posts just a couple of metres from the try line.
The Vikings went ahead in the space of three minutes, Matt Whitley going under in the centre and ghosting through a vacant Warrington defence after a kick from Lloyd White was blocked.
In the 36th minute Warrington were back to within two points of Widnes, Kevin Penny grounding the ball in the corner on the near side after a clever kick from George King.
Five minutes into the second half and Ben Currie thought he had touched down in the corner, but it was disallowed after confirmation from the video referee he had dropped the ball a metre from the try line.
At the other end, Patrick Ah Van wasted a glorious chance to score a try for Widnes as he was caught offside on the near side when looking to receiving the pass from Brown.
The Wolves moved back in front after Brad Dwyer touched down evading the challenge of White. Gidley scored the conversion to make it 18-12 with 20 minutes left to play.
Warrington were ahead for just minutes, Charly Runciman rounding off a brilliant passage of play from Widnes after a great kick return by Rhys Hanbury.
But that was as close as they got.
The Wolves took the final 20-18 lead with six minutes left, Gidley scoring the crucial penalty after Hep Cahill was penalized for a knock on.