Australian Jamie Soward, a stop-gap signing brought in to rescue the Broncos' ailing season, made his mark with a superb solo try on his third appearance as the Londoners demonstrated the gulf in standards between the bottom of Super League and the top of the Championship.
Sheffield, who were unbeaten since April Fool's Day, showed plenty of spirit but made too many handling errors to give themselves a realistic chance of replicating their heroics of 1998, when they went on to lift the trophy.
The Eagles made an inauspicious start, with scrum-half Dominic Brambani losing the ball from the kick-off in Antonio Kaufusi's crunching challenge and that set the tone for the opening quarter.
Papua New Guinea international Menzie Yere twice lost the ball inside his own half and Joe Hirst and Tom Armstrong also came up with knock-ons that put their side under enormous pressure.
Sheffield scrambled to keep their line intact and dangerous full-back Quentin Laulu-Togagae turned defence into a dangerous attack with a break down the middle which petered out when winger Scott Turner hacked the ball dead.
But the pressure finally told on 21 minutes when London stand-off Michael Witt brushed off the attempted tackle of his opposite number Pat Walker to go over for the game's first try.
Witt also kicked the goal but the Eagles hit back straight away when Yere made up for his earlier errors with a superb one-handed pass out of a two-man tackle to get Turner over at the corner, much to the delight of the 2,459 crowd.
Brambani was wide with the conversion attempt and the Broncos increased their lead on 28 minutes with Soward's solo try as he took the ball straight from a scrum and veered around two defenders before sidestepping past winger Misi Taulapapa and crossing at the corner.
Soward clearly sensed a close game as he attempted to put his side two scores in front with a drop goal five minutes before half-time but his kick rebounded off the crossbar.
Trailing 10-4 at the break, Sheffield went close early in the second half when Turner was bundled into touch just short of the line but they fell further behind on 47 minutes when Armstrong dropped the ball from Witt's high kick to present Broncos winger Michael Robertson with the simplest of touchdowns.
Witt's second goal made it 16-4 and there was no way back for the part-timers when second rower Shane Rodney and centre Rhodri Lloyd, playing on loan from Wigan, both powered their way past tiring limbs for further tries.
Soward kicked both conversions and put over a drop goal as the Broncos led 29-4 but Yere showed his strength to pull a try back for the home side on 67 minutes and Walker added the goal.
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- Michael Witt
- Super League