Defence proved to be the difference between the two sides, with too many mistakes from Leeds while Warrington held firm throughout, conceding only one try.
Instead a Warrington break down the right created field position for a superbly-placed Briers chip, the ball claimed by Atkins who dived over the line.
Leeds tried to find a way back into the game, but some soft defending allowed the Wolves to extend their advantage, Atkins slipping through the outstretched arms of Ian Kirke and Westwood converting for a 14-0 lead.
Warrington could have scored immediately after the restart with a break down the middle, but Westwood’s kick was deal with by Rob Burrow; the Wolves’ hard-working defence prevented Leeds from getting onto the scoresheet.
With sixty minutes played Warrington struck again, a Briers kick to the corner looking as though it would drift over the dead-ball line only for Hicks to claim the ball brilliantly and touch down, Westwood converting.
A few moments later Leeds were finally able to find way past the Wolves defence, Lee Smith sprinting over at the corner and Kevin Sinfield landing an impressive conversion from out wide, but there was to be no comeback.
As if that wasn’t enough Warrington reached the thirty-points mark courtesy of a try from Louis Anderson and Westwood’s third and final goal.
Leeds Rhinos – 6
T: Smith (66)
G: Sinfield (66)
Warrington Wolves – 30
T: Atkins (14, 35); Hicks (18, 62, 73); Anderson (76)
G: Westwood (35, 62, 76)
Ref: Richard Silverwood