Summer signing Paddy Kenny shone on his home debut to frustrate Shrewsbury as new-look Leeds breezed through to the next round.
But Kenny's opposite number Chris Weale was less convincing after his move from Leicester.
Weale, whose identical twin Sam was competing for Team GB in the modern pentathlon, chose to parry Rodolph Austin's 30 yard drive in the 20th minute and Luciano Becchio stabbed the ball in from six yards. Six minutes later the keeper failed to claim the ball at the feet of Ross McCormack, who passed inside for Luke Varney to fire into the unguarded net.
In the second half, skipper David Norris drove home from Varney's downward header and McCormack aimed a penalty into the bottom corner after Michael Hector handled.
In the 76th minute Leeds introduced controversial Senegalese international El Hadji Diouf, who has joined them on a non-contract agreement and needs to win over the fans.
Manager Neil Warnock said: "He trained with us on Thursday and Friday and I will make a decision on him before next weekend because if I sign him (permanently) I will want him to be involved against Wolves.
"We have no money at the moment so he won't be retiring on the wages we can offer, but he is available on a Bosman transfer and he has genuine quality. He has always been a wild card and we have had our moments in the past, but I met him at a function a few weeks ago, I told him what I disliked about him and how I felt he could improve and it was a good conversation.
"I also spoke to a few people who know him well and they told me how good he is in the dressing room."
While Shrewsbury manager Graham Turner hurried away without making any comment, Warnock said he was delighted with the outcome. He said: "It was just what we needed because Shrewsbury are a good side. They are buzzing after promotion and Paddy had to make a couple of really good saves.
"When you have the best keeper in the country you always have a chance. I wouldn't swap him for any keeper in the Premier League. It was a shock to see him spill one today because he never does that. It showed he is human after all, but he is without doubt my best signing of the summer."
There were the familiar chants of "Bates out" from those dissatisfied with chairman Ken Bates and the perceived lack of progress over selling the club.
Shrewsbury, newly promoted to League One, showed some clever touches at times and Kenny made smart saves from Mark Wright, Jermaine Grandison, Marvin Morgan and Luke Summerfield.