Albion tasted defeat on the road for just the second time this season in South Wales on Tuesday night.
Goals from Callum Paterson and Lee Tomlin either side of Charlie Austin’s leveller saw the Baggies frustrated by a side who have lost only once on home soil this campaign.
Bilić made six changes to the side that saw the Baggies through to the FA Cup fifth round at West Ham United on Saturday.
Sam Johnstone, Hal Robson-Kanu, Kyle Bartley, Jake Livermore, Romaine Sawyers and Nathan Ferguson all returned to the Croatian’s starting XI, while Dara O’Shea made his full league debut for Albion after impressing once more at the London Stadium.
The Baggies started brightly at the Cardiff City Stadium but it was the hosts who might have taken an early lead had Robert Glatzel not fired straight at Johnstone from Will Vaulks’ throughball.
Livermore flashed wide with a left-foot half-volley on 19 after the Bluebirds failed to fully clear from Phillips’ in-swinging corner.
City opted to sit deep for much of the opening half-hour, allowing Bilić’s men to dominate possession, while scoring opportunities remained at a premium.
Cardiff went close with two half-chances when Pack fired a low free-kick into the arms of Johnstone and Nelson headed wide from a long throw, before Phillips drove over from 30 yards for the Baggies.
O’Shea almost marked his maiden league outing with a goal four minutes before the interval, but the Republic of Ireland youngster flashed over at the back post after Albion put together their best move of the first half, with Edwards finding space on the left to fizz the ball across the box.
The Bluebirds were ahead within 60 seconds of the restart. Paterson slammed home from close range after Johnstone could only parry Sean Morrison’s volley from Vaulks’ long throw.
The Baggies should have been level inside six minutes. Phillips burst through a host of challenges down the right before Filip Krovinović fired inches over from the winger’s pullback.
The Croatian playmaker went close again two minutes later but Alex Smithies was on hand to make a routine save from his well-struck low shot.
Bilić introduced Charlie Austin and Kenneth Zohore just shy of the hour-mark and the Baggies were soon level. Krovinović was hacked down by Jazz Richards inside the box and Austin stepped up to send Smithies the wrong way and knock inside the right upright.
Krovinović dragged just wide of the right post from 30 yards on 64 as Albion went in pursuit of the lead.
But it was the Bluebirds who earned a 76th-minute lead with a moment of real quality - Lee Tomlin firing a 22-yard free-kick over the Baggies wall and inside the left upright.
Tomlin almost sealed it for the hosts with eight minutes remaining but after shifting on to his left foot he fired into the side netting from 12 yards.
A stoppage-time scramble inside the City box brought the home side a scare but Austin and Zohore were unable to get shots away.
But it wasn’t over yet.
Smithies had to be at his very best to deny Zohore from Phillips’ low cross with a sublime one-handed stop deep into time added on to seal three points for the hosts.
ALBION: Johnstone; O’Shea, Bartley (Furlong 77), Hegazi, Ferguson; Livermore (c), Sawyers; Phillips, Krovinović, Edwards (Austin 59); Robson-Kanu (Zohore 59).
Subs: Bond; Furlong, Brunt, Townsend, Barry.