They had to settled for three - and that may yet be the difference between making the play-offs and missing out.
They needed to win in regulation time, but instead had to battle back from 4-2 down to 4-4 to claim just one point.
Hopes of a second ended when Storm hit a winner two minutes into sudden death overtime.
On a night when nothing less than a 60-minute shift would do, Fife were slow to start, their passing was scrappy and they put themselves under un-necessary pressure with too many mistakes.
Jeff Hutchins, assistant coach, was as frustrated as the fans at the outcome.
“Last night we showed character and stuck with the game plan,” he said. “Tonight I can't say the same.
“We dipped our toe in the water, but we are fighting for our play-off lives and need to do more than that.”
Two of their goals were wiped out by equalisers within seconds - key moments in a game which saw Storm deliver a tight defensive game, and skate with some comfort after finally building a lead.
Carson Stadnyk’s opener at 4:50 was nullified by Tayler Thompson’s equaliser at 5:!0, and Storm went on to rattle the post on three occasions as they constructed a good 3-1 lead going into the second half of this hockey game.
By then the first major talking point had been and gone.
With six minutes played, Linden Springer caught Michael McNicholas with a bad hit into the boards which saw the player depart to the dressing-room for treatment.
Brandon Magee stepped up and grappled with Storm’s enforcer, but that was the last involvement for the Fife centreman as, after a prolonged effort to prise the players apart as they rolled round the ice, he was thrown out on a five plus game for fighting, while Springer sat five for boarding.
Jeff Hutchins, assistant coach, said afterwards: “I don't understand that call how he got ejected and other wasn't. That's for the league to review.”
His counterpart Ryan Finnerty was significantly more blunt in his post-game media comment.
He said he “hoped we never have to see them ref again after that display” – a point he made more forcibly at each of the stripeys as he left the ice.
If the first period was lively, the second was just scrappy.
Storm grabbed the go-ahead goal at 25:13 when a huge rebound wide to the right as simply drilled home by Joseph Hazeldine.
At 35:20 Flyers were halted on Storm’s blueline and one lightning break saw Harry Gulliver deliver a clinical finish for 3-1.
The goals sucked the energy from the building, and the lifeline Fife grabbed with a powerplay goal from Kirstian Blumenschein at 40:37 was wiped out within 30 second as Cam Critchlow’s shot flew past Shane Owen.
It took until the final ten minutes of the period for Fife to draw level.
Matt Carter turned home a fine pass from Blumenschein for 4-3 at 50:50, and then Jacob Benson then spun on a sixpence in front of the net to tie things up at 4-4 at 57:48.
Fife needed one more goal for the regulation win, but their hopes evaporated when Jonas Emmerdahl was called for boarding after a hit in the corner left Storm forward Finlay Ulrik injured. He was helped, very slowly, to the dressing-room after a delay for treatment.
That took this game into sudden death overtime, and the final word went to Storm with Adam Brady netting after a fine pass off the back boards.
On a night when Flyers could have moved off the bottom of the table, they saw the gap on Storm, in ninth, back to two points.
They also remain eight points off a play-off spot and the clock is ticking.
And while his team won the game, Ryan Finnerty departed Kirkcaldy an angry man, with a broadside against the referees which earned him a game misconduct.