A first half shot from Ralls gave Cardiff a 1-0 lead, but it was cruel on the U's as it took two deflections on its way past Sam Walker.
Two quick fire goals at the start of the second half, from Harris and Jones, made it 3-0 before Freddie Sears got a consolation for the U's.
U’s boss Tony Humes made one change to his starting eleven, an enforced one, as Cole Kpekawa came in at left back.
Ben Gordon picked up an ankle injury in the 0-0 draw at Crawley last weekend but failed to recover in time to face the Welsh side.
The U’s started the game on the front foot and home keeper Simon Moore was the first to make a save, comfortably fielding Freddie Sears’ free kick.
Sam Walker followed suit on twelve minutes, palming away a shot from home midfielder Joe Ralls.
Kaspars Gorkss went forward for a corner with twenty minutes gone but couldn’t direct his near post header on target.
There was a scare for the U’s halfway through the half, as Peter Cunningham whipped a corner in and it clipped the bar before going to safety and a goal kick.
With just over half an hour gone, the home team took the lead and it came with a huge slice of luck.
A corner was cleared and a shot from Ralls from thirty yards out took two deflections, off Gorkss and Cole Kpekawa, that wrong footed Walker in the U’s goal.
The goal didn’t upset the U’s too much and they went forward looking to get back into the game.
And only a fantastic save from Moore prevented them doing that in the thirty eighth minute, diving low to save from Gavin Massey’s shot into the corner.
The last chance of the game went the way of the hosts, but Whittingham’s effort flew straight at Walker.
It was another positive performance in the first half for Humes and the U’s, and they were more than a match for their Championship opponents.
The one goal lead was doubled on fifty two minutes for Cardiff, with an acrobatic effort from Harris.
A corner was lifted into the area and after Turner’s header went straight up in the air, Harris’ overhead kick flew into the bottom corner giving Walker no chance.
The task was made almost impossible seven minutes later, as Cardiff added a third, again from a corner kick.
Kenwyne Jones had only just come on as a sub and hadn’t had a touch before he found space and headed home at the near post.
Humes made two changes on the hour mark, bringing on Sanchez Watt for Gavin Massey and debutant Tom Lapslie for George Moncur.
Watt was straight into the action and drilled a shot just wide after linking up well with Sears.
Walker dived low to save from Noone, in what was a rare save in general play from the U’s keeper.
With seventeen minutes remaining, Sears himself gave the U’s a glimmer of hope, shooting home low via the keeper’s right hand.
The U’s top scorer picked up the ball deep, drove forward before playing a neat one two with Watt before guiding his right foot effort in.
Humes gave another youngster a debut on eighty three minutes, bringing on Dion Sembie-Ferris for Elliott Hewitt.
And he almost made a goal scoring debut, just failing to beat Moore as he looked like he was pulled back as he went for goal.
The U’s had matched their Championship opponents in general play but conceded from set pieces to go out of the cup at this third round stage.
There were plenty of positives from the performance, that need to be taken forward into the second half of the league season in the quest for League One survival.