Skipper Simon Mannering hailed his side's resilience after they held out against Melbourne's attacking threats to post a 30-22 victory in an incident-packed NRL encounter in Auckland.
Down 18-4 at half-time, the Storm got themselves back to 24-22 with five minutes to go.
But fullback Kevin Locke sealed victory for the home side when he pulled in a Shaun Johnson bomb to dot down with less that two minutes to go.
Mannering says the Warriors overcame one of the previous weaknesses by making a strong start, but knew Melbourne would respond.
"We still knew we were in a tough battle," he said.
"They came out firing after half-time and we didn't quite stick with them, but I'm proud of the guys to hang in there and finish strongly."
The Storm's well-oiled attack was menacing as they targeted the opposition's right edge.
Mannering said it was area the Warriors would have to improve as they look to push on from their seventh victory in eight matches, a run that has lifted them to the threshold of the top eight.
The Storm, sitting third on the ladder, were left ruing spurning some good chances after falling to their fourth loss in their past five outings.
Skipper Cameron Smith described his team's display as "patchy", especially in the opening spell.
"Every time we seemed to give ourselves an opportunity down their end, we just dropped it with some simple errors and we really didn't build any pressure," he said.
"The effort was there, but sometimes effort is not enough. The execution needs to be there and today it wasn't."
However, Smith also had praise for the home side's performance, which included an 85 per cent completion rate.
"You can't take anything away from the Warriors," he said.
"They were very good today. I think they deserved to win."
A crowd of 20,126, the largest at Mt Smart Stadium this season, turned up on Sunday to watch a contest that produced a thrill a minute.
The Warriors raced out to an early 10-0 lead thanks to a double from winger Ngani Laumape.
The second on 12 minutes came after a length-of-the field attack started by Locke fielding a bomb and then setting off on a 60-metre run.
Melbourne then began to gain the upper hand and were rewarded after a huge 40-20 from halfback Cooper Cronk.
The Storm scored from the very next tackle, a slick set move finished off by winger Justin O'Neill.
The visitors continued to show their menace on attack, but couldn't take full toll, letting slip three further try-scoring opportunities.
The Warriors took advantage to strike via a brilliant solo effort from Thomas Leuluai in the 32nd minute.
The little five-eighth somehow found his way past half a dozen defenders before dotting down with an outstretched hand.
Melbourne, at 18-4 down, made an electric start to the second half and two tries in four minutes - to fullback Billy Slater and centre Maurice Blair - got them right back into the contest.
With his side down 18-16, Smith elected to have a shot at goal from a penalty, but his attempt hit a post.
Against the run of play, Warriors centre Konrad Hurrell got his 10th try of the season by finishing off an expansive move.
But Melbourne set up a grandstand finish when Cronk finished off a sideline break by winger Sisa Waqa, before Locke produced his late heroics.
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