Robson's preferred strikeforce of James Beattie and Billy Sharp were given the night off as Webber and Stead seized the moment.
The Sheffield side snatched the lead in the 15th minute. Webber cut inside to drill in a stinging right-foot shot which Barry Roche could only push away and Stead picked up the loose ball to hammer it into the far corner from 16 yards.
Chesterfield were back on level terms just two minutes later when midfielder Peter Leven found space to pump over a low cross and Jack Lester, who had a brief spell at Bramall Lane, dived in bravely to plant his header beyond Paddy Kenny's reach.
Subsitute Alan Quinn, an early replacement for Gary Naysmith, almost put United back in front on 36 minutes after being set up by Stead's cheeky back heel but the little midfielder's low effort was pushed round the post by the diving Roche.
United did make it 2-1 though on the stroke of half time, centre back Lee Bromby's long ball upfield was brought down in a sweeping move by Stead who finished clinically from 10 yards.
Underdogs Chesterfield made United fight all the way with Blades old boy Wayne Allison almost levelling matters in the 52nd minute. The veteran striker stretched to meet a Philip Picken cross but his header was blocked on the line by Kenny.
It was only four minutes later though that Webber hit United's third with a stinging finish courtesy of another Bromby pass.
Blades new boy David Carney had a chance to kill off Chesterfield but fired wide of an empty goal and minutes later full back Derek Geary's fierce drive was pushed round the post in spectacular manner by the diving Roche.