The Owls had climbed above the Blades in the League One table earlier in the day thanks to a 2-1 victory at Brentford.
At Bramall Lane, goals from Joel Byrom and Scott Laird put the visitors in command before Richard Cresswell and Matt Lowton scored to set up a tense finish.
At Griffin Park, goals from Keith Treacy and Miguel Llera enough to see Wednesday past the Bees, for whom Clayton Donaldson converted a penalty on the hour mark.
The defeat ends Brentford’s hopes of reaching the play-offs.
At the other end of the table, Wycombe Wanderers conceded twice at the death to lose 4-3 at home to Notts County, relegating the Chairboys to League Two.
Playing at home and needing to win to stay in touch with Walsall and Leyton Orient, Wycombe were leading 3-2 in the 89th minute before Dele Adebola equalised for County.
And in the dying seconds winger Alan Judge scored his second of the match to send Wycombe down, keeping County in the hunt for a play-off spot.
Wycombe join Chesterfield, Exeter City and Rochdale in League Two.
A double from Ivorian striker Francois Zoko helped Carlisle keep their play-off hopes alive as the 4-1 scoreline at Brunton Park condemned Exeter to relegation.
Jordan Cook and Liam Noble were also on target for the home side with Liam Sercombe replying for the Grecians, who went down to their ninth successive away defeat.
Champions Charlton Athletic were held to a 2-2 draw by mid-table Preston North End.
MK Dons, already in the play-offs but short of an automatic promotion slot, cemented fourth place with a 2-1 win at bottom club Rochdale. Jay O’Shea and Dean Bowditch were on target for Dons, with Jean-Louis Akpa Akpro pulling one back late on for Dale.
Huddersfield, who had been behind the Dons on goal difference, slipped two points behind to fifth after a 1-1 draw at Walsall, for whom a point was enough to secure their League One status. Lee Novak’s early goal put the Terriers ahead before Florent Cuvelier equalised just after half-time.
Colchester finished their home season on a winning note with a 4-2 home victory over fellow mid-table side Tranmere. Ian Henderson, Tom Eastman, an Ian Goodison own-goal and Freddie Sears scored for the Us, with James Wallis and Lucas Akins on target for Tranmere.
Leyton Orient escaped relegation despite losing 2-1 at Hartlepool, the O’s spared by Wycombe’s collapse. Antony Sweeney put Pools ahead before Jamal Campbell-Ryce equalised. Ryan Noble headed the winner, with Orient seeing two penalty appeals rejected as they tried to level.
Bury rounded off their home campaign with a 0-0 draw against Oldham in a lively Greater Manchester derby.
In other results, Scunthorpe drew 1-1 at home to Bournemouth, both sides well clear of the relegation zone, while Yeovil beat relegated Chesterfield 3-2 to move on to 54 points.