Former West Brom striker Lee Hughes looked to have had the last laugh on the Wolves boo boys by breaking the deadlock.
Nenad Milijas equalised from the spot after County defender Liam Chilvers was sent off for bringing down Christophe Berra.
Substitutes Steven Fletcher and Doyle settled the tie in the first period of extra-time. Kevin Smith scored a late consolation before Doyle grabbed his second.
County could feel aggrieved with the outcome as the League One outfit matched their higher-graded opponents for much of the tie.
Wolves boss Mick McCarthy made nine changes from the side beaten at Tottenham at the weekend - but the replacements hardly covered themselves in glory in the bid to push for a place in the Barclays Premier League line-up.
Hughes had the ball in the net after only three minutes after getting on the end of a free-kick from Ben Davies which skidded across the box but he was adjudged offside.
Milijas was only just too high with a glancing header from Greg Halford's long throw, then County skipper John Thompson was forced to limp out of the action and was replaced by Mike Edwards after 13 minutes.
Hughes got into a good position to the left of the Wolves box but dragged his shot across the face of goal.
George Elokobi came close to breaking the deadlock after 37 minutes following a deep inswinging corner from Milijas. But his header crashed against the crossbar and rebounded back into play.
Hughes took advantage of a mistake by Mouyokolo to find himself with Wayne Hennessey to beat but the Wales goalkeeper held onto his curling attempt.
After 57 minutes Hughes gave County the lead with his fourth goal of the campaign. Mike Edwards floated the ball into the box and Hughes's looping header flew past Hennessey into the corner of the net.
He celebrated in trademark fashion by pulling his shirt over his head and earned himself a yellow card from referee James Linington.
Wolves tried to retaliate and Kevin Foley's shot on the turn flew just wide.
Hughes had the chance to seal the tie with 12 minutes remaining as Wolves were caught on the counter-attack.
He was found in space by John Spicer 15 yards out but Hennessey managed to deflect his low drive around the post.
Hughes was substituted with 10 minutes remaining and displayed a T-shirt under his club shirt bearing the words 'Boing Boing' - the chant associated with the fans his former club West Brom.
But within three minutes Wolves drew level as County defender Liam Chilvers was sent off for hauling back Christophe Berra. Up stepped Milijas to blast the penalty past Burch into the roof of the net.
Wolves needed only two minutes of extra-time to move ahead for the first time.
Doyle made a powerful break into the County box before squaring the ball across the box to Fletcher, who made no mistake.
It was Fletcher's third goal since his £7million move from Burnley in the summer.
Hennessey tipped over Kevin Smith's drive but Doyle effectively sealed the tie just before half-time in extra-time.
Doyle again teed up Fletcher, whose shot was parried by Burch before the Republic of Ireland striker converted the rebound for his first domestic goal of the campaign.
Smith pulled a goal back for County when he headed in Craig Westcarr's cross - but Doyle brushed off any doubts about the outcome when he made it 4-2 with a minute remaining from 12 yards out.