Craig Lingard’s side were aiming to make it back-to-back wins in the league for the first time this season, having recorded an emphatic 50-18 victory over Batley Bulldogs in their previous outing at the Steel City Stadium.
However, the Eagles made the trip across to West Yorkshire without several key names, including Matty Marsh and Titus Gwaze.
There were positives on the selection front, though, with loanee Harvey Horne returning at full-back, while Alex Foster slotted in at centre and Evan Hodgson came into the second row.
Bradford entered the contest in red-hot form, looking to extend their winning run to four games after a commanding 12-42 win away at Oldham last time out.
It was the home side who got the scoreboard moving at the Bartercard Odsal Stadium, with a Luke Hooley penalty in the 13th minute giving them an early lead. That advantage was stretched midway through the half as Mitch Souter dived over for the game’s opening try, putting the Bulls 8-0 up.
The Eagles burst into life in the closing stages of the first half, producing an electric seven-minute spell that saw them run in three unanswered tries. Kris Welham sparked the revival, crossing for Sheffield’s first of the afternoon before Ryan Millar and Morgan Smith followed him over the line.
Cory Aston, who continued to lead from the front with the boot, added all three conversions to turn the game on its head and put the Eagles 8-18 ahead heading into the break — with Aston’s first kick of the three also taking him past 1,000 career points in Sheffield colours.
Just minutes after the restart, Bradford found themselves temporarily down to 12 men as Elliot Peposhi was shown a yellow card for foul play. The Eagles capitalised on the advantage with Aston slotting over a penalty from in front of the posts to push the lead out to 8-20.
However, the second half proved to be a different story. Bradford regrouped and responded with a powerful spell of their own, scoring three tries in a 15-minute stretch through Jordan Lilley, Zac Fulton and Luke Hooley.
The sharp turnaround swung the momentum firmly back in favour of the home side, as they moved into a 24-20 lead with 20 minutes left on the clock.
A further penalty from Hooley extended the gap to six points, and the result was sealed when Nathan Mason crashed over in the final minutes to round off a fifth straight victory for the Bulls and consign Sheffield to a frustrating defeat on the road.
The Eagles will look to bounce back next Sunday when they travel to the capital to face London Broncos at Rosslyn Park (3pm kick-off), in what promises to be another stern test in the Betfred Championship campaign.