City took the lead after a goalmouth scramble, Scowcroft's shot hitting Rob Edwards and at least one other player on its way into the net.
And Lescott gifted them a second when he tried to clear a Marcus Hall header but sliced into his own net.
Wolves did have chances of their own but Colin Cameron hooked his shot wide while Gabor Gyepes also went close.
Wolves boss Glenn Hoddle:
"I thought it was traditional to give out your presents on Christmas Day, not New Year Bank Holiday.
"It was two own goals which cost us the game and they were both conceded from set-pieces, which is something I thought we'd ironed out.
"It doesn't matter how well you play, if you give away goals like that you make it impossible for yourself."
Coventry: Fulop, Duffy, Williams, Shaw, Hall, Scowcroft, Osbourne, Doyle (Jorgensen 90), McSheffrey (Whing 75), Adebola, John (Morrell 90).
Subs Not Used: Ince, Heath.
Goals: Scowcroft 8, Lescott 35 og.
Wolverhampton: Postma, Lescott, Craddock (Seol 61), Gyepes, Edwards, Anderton (Rosa 67), Huddlestone, Cameron (Ganea 77), Kennedy, Miller, Clarke.
Subs Not Used: Oakes, Ince.
Booked: Cameron, Huddlestone, Miller, Gyepes.
Ref: E Ilderton (Tyne & Wear).