Wolverhampton Wanderers 0 Birmingham City 1: Led Zeppelin's Robert Plant jetted in from Texas to watch his beloved Wolves, yet it was the 2,000 visitors from 20 miles down the M6 whose songs filled the air here last night.

Wade Elliott struck with 16 minutes left to ensure a Championship success over the Premier League, sending Birmingham to Sheffield United in the fourth round and leaving Wolves dazed and confused after a ninth game without a win.

The goal stemmed from a corner by Jordon Mutch. Elliott's first effort hit the post – "I did my best to miss it," he joked later – but when David Murphy scuffed the ball back towards goal, the man whose spectacular strike swept Burnley into the top flight at the expense of Sheffield United in the 2009 play-off final hooked the ball in while still on the floor to book a fourth-round reunion with United at Bramall Lane.

A good night for Birmingham, then, but another sad showcase for the FA Cup. Even with cut-price tickets, there were barely 10,000 at Molineux for a derby, while managers Mick McCarthy and Chris Hughton underlined their priorities by making 10 and six changes respectively from the weekend's league fixtures. Birmingham's reserve keeper, Colin Doyle, made fine stops in the closing minutes from Steven Fletcher and Stephen Hunt to reprise the late double save that denied Wolves at St Andrew's.

It said much about Wolves' laboured showing that McCarthy singled out rookie right-back Matt Doherty, 20, as their best player. "I'm bitterly disappointed," he said. "The result hinged on us not marking from a corner. I'm very angry, livid that we've gone out." Hughton was "very satisfied", and added: "I thought it was a good performance by us."

Wolverhampton Wanderers (4-4-2): De Vries; Doherty (Ward, 83), Stearman, Berra, Elokobi; Hammill, Jonsson (Guedioura,67), Milijas, Hunt; K Doyle (Fletcher, 72), Ebanks-Doyle. Substitutes not used Hennessey (gk), Henry, Keogh, Forde.

Birmingham City (4-4-1-1): C Doyle; Spector, Caldwell, Davies, Murphy; Redmond (Burke, 78), Gomis (Fahey, 89), Mutch, Beausejour; Elliott; Rooney. Substitutes not used Butland (gk), Zigic, King, Valles, Gnahore.

Referee H Webb (S outh Yorkshire).