The home side trailed to Graham Stuart's header just before half-time, but hit back with two goals in five minutes early in the second period. "I don't know whether I'll get the job but I'm fairly relaxed about the situation," Lee said afterwards. "I'd like to be manager, but I'd also be happy to stay on at the club under someone else. Whatever happens, I'm getting valuable experience."
After Saturday's 6-1 win at Bristol City, Wolves supporters were eager to see more signs of a post-McGhee revival, but there was never a real prospect of Sheffield United succumbing so easily and despite enjoying the greater share of possession, Wolves were restricted to two clear chances before half-time.
First David Connolly stretched out a boot to flick Steve Sedgley's long ball over the goalkeeper Simon Tracey, but Traianos Dellas prevented it crossing the line. Injured in the incident, Tracey recovered to prevent the home side taking a 43rd-minute lead when he pushed Lee Naylor's drive around his right-hand post.
Against the flow of play, United went ahead just before half-time when the wing-back Vassilis Borbokis crossed towards the near post and Stuart rose to direct a header beyond the goalkeeper Mike Stowell.
Wolves scarcely deserved to be behind but it took them less than nine second-half minutes not only to equalise, but to take the lead. First Connolly swept the ball home at the far post after Guy Whittingham, reacting quickly to a loose ball, delivered an instant cross from the right after 49 minutes.
Five minutes later, Connolly turned provider, pulling the ball back for the substitute Carl Robinson, who had been on the field just 40 seconds, to clip home Wolves' second.
Wolverhampton Wanderers (3-5-2): Stowell; Emblen, Curle, Sedgley; Green (Ferguson, 65), Osborn, Gomez (Robinson, 53), Corica, Naylor; Whittingham, Connolly. Substitute not used: Jones.
Sheffield United (3-5-2): Tracey; Dellas (I Hamilton, 65), Marker, Nilsen; Borbokis, D Hamilton (Marcelo, 73), Stuart, Woodhouse, Quinn; Saunders, Katchouro (Twiss, 73).
Referee: R Pearson (Peterlee).