The six-time championship winners have endured a torrid season, winning just four of their 21 fixtures after being deducted six points for going into administration.
And a 17th defeat of the campaign at the John Smith's Stadium consigned them to the drop along with London Broncos, whose fate was sealed last week.
Coach James Lowes promised in the build-up to the encounter that his Bulls team would fight to the death and a spirited first-half display underlined that point.
Former Giants man Luke George opened the scoring with his first of two tries after just seven minutes, but the hosts went in 26-16 to the good at the break.
And the Giants proved too strong in the second period, with Jermaine McGillvary completing his hat-trick with two tries in the final 13 minutes.
Leeds Rhinos and Castleford Tigers got the action under way in round 21 of the season as they both missed the opportunity to go top of the table with a pulsating 24-24 draw at Headingley.
Rhinos and England captain Kevin Sinfield made the headlines for the wrong reasons, with the 33-year-old being set off for the first time in his illustrious career for a head-butt on Luke Dorn eight minutes from time.
That uncharacteristic moment of madness from Sinfield proved costly, too, as the Tigers clawed back a six-point deficit courtesy of a converted Grant Millington try to earn a draw.
That result gave Wigan Warriors the chance to climb above St Helens at the summit for at least 24 hours - and they did just that by hammering Hull FC 56-10 on Friday.
George Williams' maiden senior hat-trick was the highlight of a dominant Warriors performance at the DW Stadium, with Dom Manfredi also crossing twice.
Hull now sit six points adrift of eighth-placed Widnes Vikings after they held off a second-half fightback to beat Warrington Wolves 28-14 thanks in no small part to a Jack Owens double.
Wigan's lead at the top lasted just a day as Saints unsurprisingly crushed the hapless Broncos 58-16 at Twickenham Stoop.
Nathan Brown's side ran in 11 tries to condemn the Broncos to their 21st defeat from 21 games this season, with Mark Percival, Jordan Turner and Matty Dawson all scoring two tries apiece.
Elsewhere, Catalan Dragons crushed Wakefield Wildcats 40-6 in Perpignan on Saturday - Elliott Whitehead notching a hat-trick for the French outfit - and Salford Red Devils came from 12-4 down at half-time to beat Hull KR 38-18.