Goals in each half saw Alan Pardew's men record a comfortable victory over their Championship opposition, and they will now face Manchester City in the next round
Alan Pardew's men had defeated Morecambe in the previous round, but faced a sterner test against a Leeds side renowned for causing upsets in cup competitions in recent years.
The Championship outfit gave a good account of themselves, but Newcastle were always in command, cruising to a comfortable victory.
Cisse headed in his first goal of the campaign to put Newcastle in front midway through the first half, before Yoan Gouffran wrapped things up with a fine curling strike after the break.
Newcastle made six changes to the side defeated 3-2 by Hull City in the Premier League at the weekend, with Yohan Cabaye and Loic Remy rested, while Leeds boss Brian McDermott made four alterations to the side that lost 2-1 to Burnley in their last outing.
And it was the visitors who created the first chance of the game, with Ross McCormack's chipped effort striking the top of the crossbar.
The hosts were slow out of the blocks, and it took them nine minutes to craft some sort of response, captain Fabricio Coloccini's header cleared off the line after Sylvain Marveaux's corner.
Newcastle grew into the game and they came close again as Gouffran glanced Ameobi's far-post cross wide.
Leeds refused to allow Newcastle to control the play though, and they were again unfortunate not to have taken the lead when Matt Smith's point-blank header was well saved by Tim Krul.
Still, despite all Leeds' positive attacking play, it was the hosts who broke the deadlock, Cisse heading in from close-range following great work down the left-hand side from Sammy Ameobi.
Ameobi continued to trouble the Leeds' defence, and the England Under-21 international was at the forefront of another Newcastle attack in the closing stages of the half, his delivery headed over by Mathieu Debuchy.
McDermott's side provided a persistent attacking threat throughout the contest, as Smith was denied by Krul for a second time in the early stages of the second half after he had leapt higher than Mike Williamson to direct a header towards goal.
Newcastle weathered that spell of pressure, though, and 22 minutes into the second half they secured their place in the fourth round, Gouffran collecting a pass from Ameobi before turning and firing a superb right-footed finish past a despairing Paddy Kenny and into the top corner.
Pardew's side had chances to add to the lead, substitute Gabriel Obertan was denied by Kenny before Cheick Tiote blazed over, but a two-goal lead proved to more than enough to see off the Yorkshire club.