A heroic bid by Aaron Fox's men to halt the relentless march of the Northern Irish went all the way to overtime and penalty shots.
But Giants scored the only goal in six rounds to take maximum points and land the EIHL crown.
The new champions had not necessarily deserved to win the match but you cannot argue they deserved, overall, to win the League.
Sheffield had to suffer the nightmare of seeing another team lifting the cup on their pad - but now they must recover and get ready for the Play-Offs.
Steelers went into the match having lost half of their last four home games and Fox opted to move players around the top lines in the hope of finding more chemistry improvement.
Both sets of fans in the 7,906 crowd played their part in a scintillating first period edged by the Irish.
The first meaningful action saw a huge slice of bad luck for Sheffield, Antonín Boruta's shot pounded off the visitors' post and back into play for the green shirts to race down the other end score through Mark Cooper.
Giants, the younger team on a tremendous run of form, had further chances but it was their defensive contribution that caught the eye.
Mark Garside controlled play and spread composure and confidence. Players blocked shots and filled the offensive lanes and when pucks got through to goalie Tyler Beskorowany, he was waiting - on one occasion tremendously fortunate when Matias Sointu hit his pipework.
With two games remaining in the regular season, every shift was incredibly tense.
And Steelers seemed to find another level in the middle section, Tanner Eberle scoring a top-shelf cracker 39 seconds in and Marco Vallerand striking the bar.
With the amount of pressure on Giants' rearguard, the home fans were awaiting more goals and Sheffield would have deserved that on the balance of play.
Martin Latal's speed and Robert Dowd's eye for a shot had Giants on the back foot but the second period ended at 1-1.
There was nothing to choose between the two sides in the third period.
While Lewis Hook and Sam Ruopp had chances for Belfast, Eberle and Boruta were similarly unfortunate for Steelers.
Every inch of the ice was competed for; there was little space or time for anybody to do anything creative.
There was high drama with two minutes remaining, Evan Mosey's shot pinged off the goalie and seemed to be heading over the line, but the net was bundled off its moorings.
Sheffield swarmed the net but Giants took the game into overtime and subsequently penalty shots.
Sheffield failed to convert all of their six, the Challenge Cup winners scoring in the last round to land the double.
On Saturday, Giants dominated the first half of the game, mounting an unassailable 3-0 lead.
With their first line and power play on potent form, Steelers scored a single from Tanner Eberle and never looked like getting on level terms.
Belfast were as masterly in defence as they were offensively, keeping Steelers' four top point scorers Robert Dowd, Marco Vallerand, Matin Latal and Evan Mosey off the board.