With the sound of the hooter dying away scrum-half Dominic Brambani kicked a 40-metre one-pointer.
After leading for long spells in a thrilling game, Rovers had to leave Don Valley Stadium with the consolation of a losing bonus point.
"We're s
peechless, they got us at the last minute – you can never relax," said Featherstone coach Danny Evans.
"We're disappointed but the play-offs are still within our reach."
The first half was dominated by a tough forward battle for control of the ball and possession – with Featherstone just edging the contest. Substitute forwards Matty Dale and James Houston produced big spells and scrum-half Anthony Thackeray was always a thorn in the Eagles' defence.
Sheffield opened the scoring when full-back Jonny Woodcock caught Rovers napping from acting half-back and then added the goal.
Featherstone hit back with a penalty from prop Stuart Dickens and were pinning the Eagles in their half with the pack driving forward.
Thackeray produced a great burst and dummy to score Rovers' first try and Dickens added the goal.
The Eagles came back when Brambani's high kick was collected in spectacular style by winger Danny Mills to touchdown. Woodcock added the goal.
Substitute prop Dale almost crashed over with his first touch but made no mistake when he took hooker Joe McLocklan's short pass to touchdown. Loz Wildbore added the goal to give Rovers a 14-12 lead at the break.
A dropped ball by Rob Worrincy gave Rovers possession and a bout of pressure ended with Wildbore crashing over for a try and then converting.
Eagles came back with a second try for Mills but centre Tommy Saxton extended Rovers lead with a try.
An interception and 60-metre run by centre James Ford for a try and Woodock's conversion narrowed the gap for the Eagles to two points.
Penalties from Wildbore and Dickens extended the lead but Rovers were losing the possession battle.
With seven minutes left a penalty try awarded to Brendon Lindsay and Woodcock's goal levelled the scores.
Then as the hooter sounded Brambani delivered the killer drop goal.
Sheffield: Woodcock; Mills, Ford, Reid, Worrincy; Lindsay, Brambani; Howieson, Edwards; Stringer, Szostak; Whitaker, Hayes. Subs: Pickering, Buckenham, Brown, Hepworth.
Featherstone: Wildbore; Pryce, Saxton, Dooler, Kirk; Kain, Thackeray; Tonks, McLocklan, Dickens, Field, Hirst, Hesketh. Subs: Lee, Dale, Houston, Blakeway.
Referee: R Hicks (Oldham).
Attendance: 2,107.
The full article contains 429 words and appears in EP Leeds First & County newspaper.