ALBION overcame a classic banana skin of an FA Cup tie thanks to hat-trick hero Simon Cox.
Everything looked rosy in the Baggies' garden when goals from Peter Odemwingie and Cox inside the opening 33 minutes put them 2-0 up.
However, Championship high-fliers Cardiff pulled one back through former Hawthorns striker Robert Earnshaw before the break - and sub Joe Mason levelled the tie five minutes after the interval.
But Cox secured Albion's place in tomorrow's fourth-round draw with two more goals.
His second of the match, in the 61st minute, was worthy of winning any game, beating Tom Heaton all ends up with a 25-yard piledriver.
And the Ireland forward made the tie safe in the final minute by stabbing home Odemwingie's cross from close range.
Gonzalo Jara Reyes was granted only his second start of the season as Roy Hodgson made two enforced changes. Fit-again James Morrison was also recalled, with Paul Scharner (Achilles) and Jerome Thomas (groin) making way.
In total, Hodgson was unable to call on eight senior players through injury, and that enabled Joe Mattock and Chris Wood, back from loan spells at Portsmouth and Blues respectively, to be named on the bench.
With a Carling Cup semi-final against Crystal Palace looming next week, Bluebirds boss Malky Mackay made as many as ten changes.
It was the visitors who recorded the first effort at goal - after just 35 seconds.
George Thorne, making his senior Hawthorns debut, gifted possession to Cardiff and Rudy Gestede advanced goalwards before firing over from 20 yards.
Moments later, Craig Conway curled a 25-yard free-kick straight at Ben Foster.
But Albion soon found their feet and had loud penalty appeals turned away in the fifth minute when Morrison's low cross appeared to strike the grounded Dekel Keinan's arm.
From Graham Dorrans' ensuing corner, Cox sent a half-volley high into the Smethwick End.
Yet the Baggies only had to wait until the seventh minute to break the deadlock when Craig Dawson unwittingly sprung the City offside trap with a clearance that put the predatory Odemwingie clean through.
The Nigerian made no mistake, calmly stroking the ball past Heaton from just inside the box.
Albion continued to control proceedings but Morrison and Dorrans both failed to trouble Heaton's goal with long-range efforts.
The early breakthrough had set up an exciting cup tie, with Cardiff piling men forward at every opportunity.
However, Foster remained untested as the half passed its midpoint, although Darcy Blake was unlucky to see a 25-yard volley flash three yards wide.
In the 28th minute, Billy Jones did well to get in the way of Conway's shot inside the box from Gestede's head down and divert the ball wide for a corner.
But Albion were 2-0 up just five minutes later. Nicky Shorey, who had kept the armband for the second game running in Chris Brunt's absence, was harshly booked for taking a free-kick too quickly. However, with his re-take, the left-back curled a sublime ball into the Cardiff box and Cox headed home from eight yards.
However, Shorey went from hero to villain in the space of three minutes. The former Reading man was caught dallying on the ball by Filip Kiss whose low cross was turned home by Earnshaw to make it 2-1.
Albion immediately set about restoring their two-goal cushion and Heaton did well to push away Dorrans' ferocious 15-yard drive after forceful play by Jones down the right.
Cardiff were the next to threaten. After Foster had rushed off his line to halt Earnshaw's progress, the loose ball broke to Gestede who was denied a shot at goal by Jones' last-ditch tackle.
The final action of an intriguing half saw Cox's deflected 25-yard drive fly straight at Heaton.
Albion started the second 45 on the front foot and Cox was denied a simple tap-in by Keinan's interception after a great run by Morrison.
But the Baggies' lead had been completely wiped out just five minutes into the second half.
Sub Mason controlled and turned on Earnshaw's low centre in one swift movement before clipping the ball past Foster and in off the far post.
Back came Albion and Shorey was mightily unlucky to see his 25-yard rocket smash the top of the Cardiff bar.
Hodgson made a double switch on the hour-mark, replacing Thorne and Jara Reyes with Marc-Antoine Fortune and Somen Tchoyi.
It took Fortune less than a minute to make a telling impact.
The French Guyana striker did well to hold the ball up and lay it into the path of Cox, who smashed an unstoppable 25-yard shot past Heaton and in off the far post.
Albion were now oozing confidence and a slick interchange between Cox and Fortune resulted in the latter firing into the side-netting from just outside the box.
The game was far from sewn up, though, and Foster did well to hold onto an awkward shot from Blake in the 69th minute which bounced right in front of the Albion No.1.
Just a minute later, Conway squeezed over a cross from the left and Kiss headed well wide at the far post.
Albion could have wrapped the tie up on 73 when Dorrans burst through the middle, but the Scot over-cooked his pass to Fortune and Heaton was able to save at the striker's feet.
Another chance went begging on 79 when Tchoyi slipped in Morrison, who rounded Heaton. The angle to the open goal remained tight but that was no excuse for Morrison's poor finish, as he hacked the ball wastefully into the side-netting.
Cardiff almost made him pay seconds later when Kiss planted a great headed chance straight at Foster.
Albion's wastefulness continued four minutes from time when Odemwingie controlled Shorey's centre in the box before blazing over from ten yards.
The hosts had another minor scare when Kiss let fly in the box in the 89th minute but his shot hit a Baggies defender and rolled into Foster's grateful arms.
Fortune missed another great chance seconds later before Cox finally put Albion clear with his third of the game, slotting home Odemwingie's low cross from six yards.
ALBION (4-4-2): Foster; Jones, McAuley (Tamas 75), Dawson, Shorey; Jara Reyes (Tchoyi 60), Thorne (Fortune 60), Dorrans, Morrison; Cox, Odemwingie. Subs not used: Fulop (gk), Mantom, Mattock, Wood.
CARDIFF (4-4-2): Heaton; Quinn, Keinan (Wharton 70), Blake, Naylor; McPhail, Gerrard, Kiss, Conway; Gestede (Mason 42), Earnshaw. Subs not used: Marshall (gk), Gyepes, Evans, Oshilaja, Ralls.
GOALS: ALBION - Odemwingie (7), Cox (33, 61 & 90). CARDIFF - Earnshaw (36), Mason (50).
BOOKINGS: ALBION - Shorey (unsporting behaviour 33), Morrison (foul 45+1). CARDIFF - McPhail (foul 9).
REFEREE: L Probert (Gloucestershire).
ALBION STARMAN: Simon Cox.