Wolves' new £1.5million striker Freddy Eastwood again showed his liking for the knockout competition as he marked his debut with a goal to help sink battling Bradford at Molineux.
After a woeful display in the opening 45 minutes, Wolves came to life in explosive fashion by scoring twice in 180 seconds at the start of the second half.
Eastwood, whose Carling Cup goal for Southend United last season knocked out Manchester United, broke the deadlock in the 46th minute before Jody Craddock doubled their advantage with a spectacular volley.
It was rough on the Yorkshire side, who were left to wonder what might have been.
But, to their credit, Bradford refused to wilt and they ensured Wolves endured a nervy final 12 minutes when Kyle Nix scored from six yards.
He pounced in the 77th minute after on-loan Gillingham striker Guylain Ndumbu-Nsungu had seen his shot blocked.
Bradford had been the far more threatening side in the first half, but it was the finishing of the teams that proved to be the deciding factor.
Wolves took full advantage of that escape and when Andy Keogh helped on a cross from Stephen Ward in the opening moments of the second-half, Eastwood was on hand to head the ball home from six yards.
The Bantams were still reeling from that setback when their fate was sealed three minutes later.
The Bradford defence only half cleared a corner from Kightly and the ball fell invitingly to Craddock whose first-time volley from 20 yards whistled straight past Donovan Ricketts.
Goals from Michael Bridges, Richard Garcia and Steve McPhee ensured Hull a comfortable 3-0 passage against League One outfit Crewe at Gresty Road.
Bridges who put the Tigers on the way to victory after debutant Tom Pope was penalised for handling Michael Turner's cross, although the former Sunderland and Leeds striker had his spot-kick saved by Ben Williams.
But he followed up to finish the rebound two minutes before the interval.
It made up for an earlier miss by Bridges when he half-volleyed tamely at Williams after a searching cross from Stuart Elliott had found him unmarked at the back post.
The Tigers doubled their advantage when a neat interchange between Bridges and Nicky Featherstone released Garcia, who strode into acres of space before unleashing a 25-yard drive high into the top corner.
Hull rubbed in their superiority, in terms of their clinical finishing at least, with a third goal after 70 minutes.
A misunderstanding between Chris McCready and keeper Williams allowed McPhee to wriggle in and flick the ball into an unguarded net.