The Magpies’ return to the top flight was confirmed ahead of the game after Nottingham Forest failed to beat Cardiff.
Richard Cresswell’s header which took a deflection off Darius Henderson on the line gave the Blades a 22nd-minute lead at St James’ Park, but Peter Lovenkrands levelled with a penalty on the stroke of half-time and Kevin Nolan scored the winner 17 minutes from time.
Peterborough’s one-year stay in the second tier is over after a 2-2 draw at Barnsley.
Posh, who are expected to name Gary Johnson as their new manager today, knew only a win would keep their season alive.
Iain Hume cancelled out Ryan Bennett’s early opener for the visitors but Peterborough looked set for three points when Tommy Rowe netted 13 minutes from time.
But Hume grabbed a second equaliser seven minutes later to send the visitors down with four games remaining.
West Brom could have been promoted had they beaten struggling Watford and other results gone their way but in the end they needed a last-gasp equaliser from Chris Brunt to draw 1-1 after Danny Graham had put the Hornets in front.
Watford are now above the relegation zone only on goal difference after a 3-1 win for Crystal Palace over Preston. Paul Hart’s side began the day in the bottom three and went behind at Selhurst Park, with Keith Treacy netting after only eight minutes.
But Neil Danns drew Palace level five minutes before half-time and they took the lead through Darren Ambrose’s after 50 minutes. Calvin Andrew made the points safe six minutes from time.
Sheffield Wednesday were the day’s big losers as they dropped into the bottom three following a 1-0 defeat by Bristol City at Hillsborough, Nicky Maynard netting nine minutes from time.
Second-bottom Plymouth are four points from safety after a 2-0 loss to Middlesbrough.
Stephen McManus put the visitors ahead after 22 minutes but the hosts should have drawn level just before half-time when Justin Hoyte handled in the area only for Alan Judge to see his penalty saved by Brad Jones.
And Boro made sure of the points in the last minute through Jonathan Franks.
Leicester got their promotion challenge back on track with a thumping 4-0 win over QPR at the Walkers Stadium. Martyn Waghorn scored twice with Andy King and Steve Howard getting the others.
Swansea bounced back from their derby defeat by Cardiff with a 3-0 victory over Scunthorpe, who are now only two points above the relegation zone.
David Edgar netted the opener 27 minutes in before Ashley Williams (51) and Shefki Kuqi (80) made the points safe.
Blackpool are right on the tails of their play-off rivals after a 2-0 win over Doncaster, DJ Campbell (27) and Stephen Dobbie (67) the scorers.
Reading and Ipswich emerged victorious from their midtable battles against Coventry and Derby respectively.
Grzegorz Rasiak (15), a Simon Church penalty (22) and Jimmy Kebe (40) ensured Reading had the points wrapped up by half-time at the Madejski Stadium.
At Pride Park, Gareth McAuley opened the scoring after only four minutes for Ipswich. Carlos Edwards grabbed a second (81) but Rob Hulse (83) seemed to have made it a nervous finish only for Connor Wickham to make it 3-1 in injury time.