Cisse's drought finally ended 31 minutes into a pulsating encounter when he powered a header past goalkeeper Paddy Kenny to end a run stretching back to the 1-1 Europa League draw with Benfica on April 11.
But the tie remained in the balance until deep into the second half when strike-partner Yoan Gouffran blasted home to wrap up a win over the Sky Bet Championship side.
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.
But ultimately it was Newcastle's finishing which won the day to the delight of a crowd of 36,220, who united to chant the name of Gary Speed 11 minutes into the game.
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 his 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.
Newcastle might have been behind within five minutes after dangerman McCormack escaped the attentions of central midfielder Vurnon Anita and worked his way into a shooting position.
However, as Krul prepared for the seemingly inevitable thunderbolt, the midfielder sent a deft chip over the Dutchman's despairing leap, only to see the ball come back off the crossbar.
The Magpies could have opened the scoring five minutes later when Mathieu Debuchy picked out Cisse with a right-wing cross.
But the striker, whose barren spell had extended to 11 games, miskicked with his right foot and, for good measure, did so with his left as the ball dropped invitingly once again.
Coloccini had a 14th-minute header hacked off the line by Smith, but Cheick Tiote had to throw himself into the path of Alex Mowatt's goal-bound volley six minutes later.
The Argentinian was relieved to see his glancing header from McCormack's cross drop wide after hitting the unwitting Smith in the chest at the far post, but as the half wore on, the Magpies started to gain control.
Newcastle eventually took the lead 14 minutes before the break when Dummett and Ameobi answered his call to prove themselves worthy of places in the first team set-up.
Full-back Dummett's long ball down the line allowed Ameobi to send in the perfect cross for Cisse to head firmly past Kenny.
Pardew was incensed by his side's inability to retain a lead at the weekend, and they were almost caught out once again within four minutes of the restart when Mowatt was allowed time and space down the left, although he wastefully sent his cross out for a goal-kick.
Sylvain Marveaux was equally profligate for the home side seven minutes later when he drilled a free-kick straight into the Leeds wall, and he sliced a 58th-minute shot wide after tenacious foraging by Tiote.
But the game was effectively won nine minutes later as Gouffran accepted Ameobi's pass and rolled defender Scott Wootton before thumping a right-foot shot past Kenny.
Substitute Gabriel Obertan had two opportunities to extend the lead as time ran down but on both occasions, was denied one-on-one by Kenny.