Australia require a record 412 runs to win the first Ashes Test after England took complete control on day three at the Swalec Stadium.
Ian Bell and Joe Root both made 60 while putting on 97 for the fourth wicket as the home side made 289 all out in their second innings and built a handsome lead heading into the final two days of the match.
Earlier, Australia lost their final five wickets for just 44 as they were bowled out 122 runs behind England as James Anderson finished with figures of 3 for 45.
Australia took a flurry of late wickets, as England lost their last five wickets for 53 runs, to give themselves a glimmer of hope of chasing down a total which would be the highest to win an Ashes Test, and third highest in the history of the longer form of the game.
But the reality is England hold all the aces with six sessions of the game remaining, knowing they will bowling on a surface which produced 15 wickets on day three against an Australian team who toiled in their first innings.
With overhead conditions making it a perfect morning for batting, Australia had designs on restoring parity and matching England's first innings total of 430.
However, as England discovered reverse first with the old ball and then with the new, the hosts took a near-unbreakable hold on the opening Test.
Shane Watson (30) was the first to go to Stuart Broad, as the Aussie all-rounder was dismissed via lbw for the 28th time in his career from the fourth ball of the day, despite the review showing the ball was only at the top of leg stump.
Mark Wood had his second wicket of the innings when he too trapped nightwatchman Nathan Lyon (6) with Australia having only added a single to their overnight total.
Brad Haddin, a thorn in England's side in each of the last two Ashes series, made a quick-fire 22 but Anderson had the wicket-keeper batman caught behind before Mitchell Johnson (14) clipped to Gary Ballance off Stuart Broad in the next over.
Anderson took his third wicket to dismiss Mitchell Starc for a duck to give England a healthy 122-run lead and leave Australia, who made just 308, reeling just two days after they had taken early control of the Test.
Though Starc continues to be hampered by an ankle injury suffered on day one, the left-armer dismissed captain Cook in the seventh over as he edged to Lyon at backward point.
England added just one run after lunch before losing their second wicket as Ballance failed to resist flicking a Josh Hazlewood bouncer into the gloves of Haddin.
As Michael Clarke continued to place attacking fields, England began to find the gaps as Adam Lyth and Bell made 36 in three overs to deflate Australia's early encouragement.
From Lyon's second over England were reduced to 73 for 3 when Lyth gloved one which turned outside off-stump to Clarke who at a wide first slip produced a fine one-handed catch.
But the moment of brilliance only worked to emphasise how far Australia were behind the eight ball and Bell piled on the agony with some breathtaking drives, as his recent form became a distant memory.
New man Root was in similarly good form and the pair put on 97 in 20 overs but after tea Bell went in innocuous circumstances when he was bowled by Johnson, who took his first wicket of the series in a scalp that was met with ironic cheers from the now inebriated Cardiff crowd.
Root was unable to become the first England player two centuries in an Ashes Test when he played on off Hazlewood.
Despite the stream of wickets, England were by now over 300 ahead and close to putting Australia out of sight with over two days of play remaining.
An indication of England's relaxed manner came as they lost two wickets in the space of six balls first as Buttler's miss-timed reverse sweep off Lyon looped into the hands of Haddin and then when Stokes dragged-on off Starc after an expansive looking drive.
The hosts lost a third wicket in the space of 15 balls when Broad (4) scooped the ball up towards Hazlewood at long-on and from cruising towards a lead of 400, England were suddenly required to take some time out of the match.
Moeen Ali (13) and Wood (32 not out) played with freedom, producing a series of boundaries both sides of the wicket, as the lead build into record territory and though the former and Anderson were both dismissed, the lead ensures England enter the weekend as the overwhelming favourites to take a 1-0 lead in the series.