Newcastle survived an early scare, Ross McCormack's chip looping over Tim Krul only to see his shot come back off the crossbar, but took the lead after half an hour.
Yoan Gouffran scored his first home goal to put the game beyond doubt, firing a shot from the edge of the box and past Paddy Kenny.
Newcastle had admitted in a fans' meeting the evening before the game that the cups "were not a priority" for the club, but Alan Pardew still named a strong side, with Mike Williamson the only player selected who is yet to make a Premier League appearance this season.
Meanwhile, Leeds manager Brian McDermott made four changes from the team that lost at home to Burnley, with Matt Smith and Dominic Poleon starting in attack.
Leeds gave as good as they got for long periods with powerhouse frontman Matt Smith causing all kinds of problems for defenders Fabricio Coloccini and Mike Williamson - and the visitors were only denied an early lead by the crossbar after Tim Krul saw Ross McCormack's delicate effort sail over him.
Both goals were created by midfielder Sammy Ameobi as he made the most of the opportunity afforded to him by manager Alan Pardew.
It was Ameobi's inch-perfect cross which handed Cisse a regulation chance to score by the standards of is early form on Tyneside, and his pass from which Gouffran turned his man and fired home with 67 minutes gone.
Pardew had demanded a significant improvement on Saturday's performance against Hull when despite twice taking the lead, the Magpies lost 3-2 and in the process passed up a golden opportunity to win three successive Barclays Premier League games.
He nevertheless made six changes to the side which started against the Tigers, two of them handing chances to youngsters Paul Dummett and Ameobi, and his new-look side found themselves engaged in a full-blooded cup-tie from the off.
However, Pardew will have been delighted with the way they stuck to their task to finally see off Leeds and deny Brian McDermott, the man he gave his chance in the game at Reading, a Premier League scalp.
Finally, there was a heartwarming moment after 11 minutes, when both sets of fans stood as one to applaud and pay tribute to Gary Speed, star midfielder for both clubs, who passed away almost two years ago.