Albion fought back and equalised in first-half injury time through Gianni Zuiverloon.
The Bluebirds were unchanged from the side beaten by Chelsea in the FA Cup, but injuries and suspensions forced the Baggies into four changes in their starting line-up.
City had the first strike on goal when Aaron Wildig dispossessed Frank Nouble before sending Chris Burke away. He found Gavin Rae but the midfielder scuffed his shot well wide.
In the seventh minute Jay Bothroyd was brought down inside the area by Jonas Olsson and Whittingham crashed the spot-kick into the net for his 19th goal of the season.
Midway through the half Luke Moore combined with Andwele Slory and the Dutch winger hit the inside of the far post with a low shot but the loose ball was hacked clear.
The Bluebirds suffered a blow in the 27th minute when Whittingham left the field to be replaced by Ross McCormack.
City's front two were causing the visitors defence problems whenever the ball went into the Albion half but it was the Baggies who claimed most of the possession.
They drew level in the third minute of time added on when Zuiverloon scrambled the ball over the line after Graham Dorrans had split the defence with a pass into the danger area.
The Bluebirds knew they had to work even harder in the second period and both Dorrans and Robert Koren received yellow cards as City dug deep to unsettle the visitors.
Olsson missed a glorious chance to put his side in front on the 70th minute when he headed a Zuiverloon cross over the bar from point-blank range.
Six minutes from time Burke sent a shot spinning just wide of the far post and then in the final minute he popped up on the goal-line to hack clear a goalbound shot from Simon Cox.
External Reports
Cardiff City Official website
The Guardian