Webber powered a 68th-minute Nick Montgomery cross past the helpless Steve Harper to hand the Blades their first away goal in the league and a first victory in four games and send the Magpies into 19th place in the league table.
It was scarcely more than the visitors deserved as they punished a woeful performance by Roeder's men, who have not won a league game on their own pitch since the opening day of the season.
Newcastle were second best throughout two days after their UEFA Cup heroics in Palermo and barely created a chance of any note as Charles N'Zogbia's mishit 30th-minute cross which hit the bar represented their best effort.
wThe crowd vented their anger on chairman Freddy Shepherd and his board as another three points were allowed to slip away, and boos once again resounded around St James' on the final whistle.
The Magpies head for Watford in the Carling Cup on Tuesday night in their third match inside six days, but both that competition and Europe are minor considerations when compared to their plight in the league.
The Magpies face a trip to Manchester City next weekend having taken just a single point from home clashes with Charlton and Sheffield United and knowing a vast improvement is required, and quickly.
Having won just one of their previous five Premiership games at St James' and none since the opening day of the season, there was only one requirement this time around no matter how it came.
However, the jeers which rang around the stadium at half-time told their own story as the euphoria of Thursday night's gutsy UEFA Cup victory dissipated in a cesspit of mediocrity.
Much of the credit for that had to go to Blades boss Neil Warnock, who sent out his team to harry and press and saw them do just that to leave the Magpies struggling to establish any kind of rhythm despite making six changes from their midweek side.
Even the normally ebullient Scott Parker found himself becalmed in a midfield battle in which, but for a brief spell when he and Nicky Butt got the better of Mikele Leigertwood and Montgomery, went largely the way of the visitors.
If the visitors' work-rate was impressive, they lacked the cutting edge to build upon in with Stephen Carr's interception of Webber's fourth-minute cross ahead of Alan Quinn and Rob Hulse's shot on the turn eight minutes later their only real half-chances.
But Newcastle, with Giuseppe Rossi and Damien Duff once again paired in attack, fared little better.
Titus Bramble headed a 10th-minute Duff corner well wide and Parker drilled a long-range effort into Paddy Kenny's midriff two minutes before the break.
And it was perhaps significant that the closest the home side came to breaking the deadlock was when N'Zogbia's 30th-minute cross sailed over Kenny and clipped the crossbar.
Roeder made his move at the break, withdrawing Butt and N'Zogbia, who both started in Sicily, and sending on Emre and Nolberto Solano with James Milner switching to the right.
Quinn sent a right-foot shot across the face of goal within three minutes of the restart with the visitors showing few signs of surrendering the point with which they arrived on Tyneside.
Indeed, they looked the more likely to score, Bramble coming to the rescue after Montgomery was presented with possession in the box after former Magpie Keith Gillespie recycled a 53rd-minute Derek Geary cross.
Quinn chanced his arm with an effort from distance seconds later, but Harper had to save from Webber's dipping 58th-minute shot and then saw Leigertwood hammer a left-foot drive over.
Roeder attempted to freshen things further with his final change when he sent of Thursday night's goal hero Albert Luque for Milner and begged him to pay a huge slice off his £9.5million transfer fee.
But within a minute, his hopes were ripped apart when Montgomery crossed from the right and Webber stooped to plant a firm header past Harper to put the Yorkshiremen in front.
Emre dragged a 74th-minute shot across the face of goal, but the home side's efforts to drag themselves back into the game were tepid to say the least.
Indeed, they might have lost even more heavily had Harper not managed to get a touch on Quinn's 86th-minute shot and then claim the rebound as the ball came back off the post.
The reaction when the final whistle sounded was entirely predictable and left Roeder and his players in little doubt as to how their efforts had been received.