The trio all found the net twice on a dominant night for the hosts, with Scott Conway and Matt Foley also on the scoresheet as Adam Keefe's men restored their four-point lead at the top of the standings with three games left to play.
Conway gave the Giants the perfect start after just 30 seconds as he was set in one-on-one by Owre and made no mistake with the finish over Matt Greenfield's shoulder (1-0), and their lead was doubled at 9:50 on the powerplay as Brandon McNally sat for boarding and Owre finished the rebound off Mark Cooper's initial effort. (2-0)
The Steelers responded at 11:21 when former Giants forward Brendan Connolly set up Brett Neumann in front and he beat Beskorowany on the backhand (2-1), but the home side took control towards the end of the period.
Two goals in 33 seconds put them in a commanding position as Mark Cooper restored their two-goal lead at 14:03 when he batted a puck out of mid-air and snapped one into the top corner (3-1) before Ben Lake dropped the puck back to Foley for a beautiful finish at 14:36 for the fourth. (4-1)
Sheffield ran into further penalty trouble at the end of the period as both Jonathan Phillips and Kevin Schulze sat for slashing, but the Giants were unable to further add to their lead.
The Giants' penalty kill impressed on its first outing as Conway was called for cross-checking just 58 seconds into the period but they kept the puck off Beskorowany for the entire two minutes, however they survived a scare shortly after when Daniel Ciampini turned and fired off the crossbar.
But it would be the Giants who would add on as Norris got in on the scoring, the winger going on the breakaway with Ciaran Long and delivering a sumptuous backhand finish through Greenfield's five-hole at 30:30. (5-1)
A potential Belfast powerplay was cancelled out as Brendan Connolly's hooking call was cancelled out by Conway's slashing penalty, while the Giants needed to play out another penalty on Mark Garside for delay of game after he closed his hand on the puck along the boards.
But when they returned to full strength, the hosts added a sixth just before the second intermission, Conway setting up David Goodwin for the shot and, although Greenfield made the initial save, Owre was there for the sharp angle rebound at 38:52. (6-1)
Former Giants forward Brendan Connolly pulled one back at 41:35 for the visitors (6-2) and then hit the bar on the next shift, but the fightback was short-lived as a beautiful passing move between Conway and Mark Cooper led to the latter tapping in for the seventh at 48:32 to put the result to bed. (7-2)
However, the game turned sour when Sam Jones - who had hit the bar with a shot shortly before - checked Foley to the head and prompted a skirmish in front of the Steelers bench which eventually saw the Sheffield defenceman ejected, with Owre and McNally also kicked for their roles in the aftermath.
But the Giants fans were the ones celebrating at the final buzzer, and all the more so after Norris made it his first multi-goal game in a teal jersey when he was hooked back by Niklas Nevalainen when through on goal but scored the resulting penalty shot at 58:03 to round off the scoring. (8-2)
Next up, the Stena Line Belfast Giants take on the Manchester Storm at The SSE Arena, Belfast on Saturday 25 March. Tickets are on sale HERE!