Halfback Shaun Johnson was again in sublime form for the Warriors, having a hand in their first four tries before sealing the win with a typically brilliant individual try and kicking a minutes from fulltime.
The result gave the Warriors three straight wins for the second time this season - their first over a side above them on the ladder - and saw them leapfrog the Storm, Rabbitohs and Dragons into fourth place, while extending the visitors' losing run to four matches.
Tries to Tui Lolohea, David Fusitu'a and Bodene Thompson helped the Warriors to a 16-0 halftime lead before a compelling and see-sawing second-half unfolded in front of 17,278 fans.
A resurgent Storm roared out of the sheds to post two quick tries in the left corner through Marika Koroibete and Kenny Bromwich, before Lolohea finished one of the tries of the season to give the home side breathing space.
The Storm kept coming however, Bromwich claiming a second to leave them eight adrift before the Warriors regained their focus and composure, with Johnson's converted try restoring a 14-point margin before a penalty goal capped the scoring six minutes from fulltime.
The home side registered first points in the 11th minute when Johnson put Fusitu'a away, with the centre passing out for Lolohea to score beside the posts but Johnsons kick sprayed wide.
The Storm then threatened out wide on both sides, first through Koroibete on the right before Cronk's cross-kick found left wing Richard Kennar, but desperate defence from Wright and Tomkins prevented him from grounding the ball ingoal.
The visitors were finding it hard work in the middle as the Warriors defended aggressively to restrict their go-forward, with Mannering leading the way for the forwards, and Fusitu'a reading the opposition's attack well in midfield.
The 20-year-old then claimed his try when a midfield raid saw Johnson and Tomkins combine to send him diving into the corner to make a one-handed put-down, with Johnson converting from touch for a 10-0 lead.
They added to their tally when a quick play the ball helped Johnson to put Thompson through a hole; the back-rower beating Munster for the third try, with Johnson again converting to make it 16-0 five from halftime.
The Storm looked certain to cross in the dying stages of the half but were twice denied by Wright, when he prevented the ball from reaching Kennar and then bundled Chambers into touch, to maintain a clean-sheet for the half.
The Storm eventually crossed after an energetic start to the second-half, with Cronk's curving kick finding Koroibete to plant the ball down but Smith's conversion attempt from touch was waved away.
Mistakes and penalties saw the Storm improve their share of possession and the Warriors were made to pay when Kenny Bromwich barged over to scored twice in quick succession to leave them eight adrift with 26 minutes remaining.
Any doubts over the Warriors' premiership credentials were then dispelled when Lolohea finished a dazzling effort before Johnson stepped through on a trademark run to score the fifth try.
A field goal looked on the cards when the Warriors were awarded a penalty, Johnson adding the two to seal back-to-back home victories for the first time this year.
Warriors 28 (Lolohea 2, Fusitu'a, Thompson, Johnson tries, Johnson 3 cons, 1 pens), Storm 14 (Koroibete, Bromwich 2 tries, Smith 1 con).
