Wolves were given a couple of reprieves following some uncharacteristic disjointed defending early on but Podence opened the scoring inside the first quarter of an hour and, from there, the hosts hardly looked back.
They had to wait until the 72nd minute for Semedo to double their lead before Podence grabbed his second soon after, the forward’s first goals since scoring in the Carabao Cup defeat against Tottenham on September 22.
Billy Sharp thought he had equalised before half-time but the goal was chalked off for a high foot as the Blades endured an unhappy return to the ground where their relegation from the Premier League last season was confirmed.
The Championship side had won all three of their previous fixtures since Paul Heckingbottom took charge but this was their first outing since December 20 following several postponements and some of the team appeared rusty.
Both sides made five changes to their line-ups, with Wolves, four-time winners of the competition, handing a rare start to the impressive Fabio Silva, although they were on the back foot in the early forays.
Only leaders Manchester City have conceded fewer than Wolves’ 14 goals in the Premier League this term but Bruno Lage’s side were sloppy early on and the returning Rayan Ait-Nouri should have been punished for a wayward pass.
Instead, Sharp dragged wide before strike partner David McGoldrick spurned another couple of chances, first glancing a header off-target when unmarked and then shooting straight at Wolves’ back-up goalkeeper John Ruddy when given time to choose his spot, with Conor Coady clearing a loose ball trickling towards goal off the line.
Where Sheffield United failed to capitalise on individual mistakes, Wolves succeeded. There looked to be no danger following a hopeful ball over the top but Blades defender Jack Robinson made a hash of a clearance, gifting possession to Silva and his lay-off led to Podence assuredly firing beyond Wes Foderingham after 14 minutes.
Wolves largely dominated the rest of the half, although Adama Traore fired wastefully over after being teed up by the influential Silva, who was denied by the fingertips of Foderingham following a clever one-two with Podence.
Sharp seemed to drag Sheffield United level before the interval after getting ahead of Coady at the back-post and hooking into the net but the Blades captain’s high foot meant Wolves were given a let-off.
Lage, a former Sheffield Wednesday assistant under Carlos Carvalhal, shored up his midfield for the restart as Joao Moutinho was introduced, while Robinson was unsurprisingly hooked at the break after an error-strewn display.
Shortly after Raul Jimenez and Francisco Trincao were introduced into the fray midway through the second half, Wolves doubled their lead, with Sheffield United’s defenders on their heels following Podence’s ball forward.
Ait-Nouri, starting for the first time in four weeks after a groin injury, hared on to the ball down the left and squared for Semedo to finish beyond Foderingham before Podence made sure there was no way back for the visitors.
Foderingham raced out of his goal in an attempt to gather but was beaten to the ball by Jimenez, who calmly rolled back to allow Podence to fire into an empty net in the 80th minute and guarantee Wolves’ safe passage into the next round.
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