The game, which Steelers had twice led, went to penalty shots.
All were missed from both sides, other than Manchester's Rob Linsmayer, who wrapped up the road victory.
The pair had met in a Challenge Cup game Group A fixture, with only Robert Dowd missing from the home side's line-up.
Storm were without last season's top scorer Mike Hammond.
Without the talisman forwards, both sides were unable to find a goal in the first period.
Storm dominated at the start, with the effervescent Evan Richardson hitting the outside of Jackson Whistle's post in the first few seconds.
Sheffield's most memorable moment came on a 72-second five on three penalty kill, which they protected their cage with great skill and energy.
It was only in the closing minutes of the session, with Steelers on the powerplay, that Josh McFadden hit two stinging drives into Matt Ginn's goalie pads.
Tanner Eberle had two chances on breakaways but the breakthrough came from a defenceman.
Matt Rupert played a cute pass inside to Yiri Gula and his wrist shot ripped across Ginn and into the roof of the net, at 28.50.
Jonathan Phillips was also an assist-provider.
Storm came back though and with 56 seconds of the period remaining Luke Moffatt equalised, after sloppy defensive play.
While Sheffield had generally improved, they were back to square one, again.
But Evan McGrath's lethal drive from the left flank made it 2-1 at 43;07.
Peculiarly, the match went into a lull, the crowd were quiet and Storm seized the opportunity.
Dane Byers had a chance and them Moffat unselfishly teed up Ciaran Long for the 2-2 equaliser.
Overtime, despite a rash of chances at both ends, failed to separate the clubs.
Steelers had five attempts at scoring a penalty shots - and failed to find the net, ensuring Storm went back over the Pennines with a win under their belt.