Goals either side of half-time saw the Premier League newcomers see off the dogged Spanish side, with the striker scoring and assisting in a fine all-round performance
Whittingham rifled home a long-range effort in the first half after collecting a pinpoint pass from Campbell, and provider turned goalscorer after the interval as the striker rounded goalkeeper Gorka Iraizoz to double the hosts' lead.
Andoni Iraola's volleyed effort reduced the arrears, but Cardiff held on to secure victory in their final pre-season friendly.
The hosts had to withstand some heavy pressure at times, with Ander Herrera and Markel Susaeta providing a threat for the Spanish side.
They signalled their intent midway through the first half, Benat striking the crossbar with a 20th-minute effort that left David Marshall stranded.
But Malky Mackay's side maintained their composure and took the lead when Whittingham, the recipient of a superb pass from Campbell, fired an unstoppable drive into the bottom corner from 20 yards out.
They extended their lead just seven minutes into the second half, with Campbell racing clear, skipping past the keeper and rolling into an empty net.
But Bilbao refused to lie down and just four minutes later they were back in the contest as Iraola struck a firm volley past Marshall from inside the box.
Enrique Sola spurned a chance to level the scores, firing well over the bar in the closing stages.
Whittingham was similarly wayward with a long-range strike as Cardiff closed their pre-season campaign with a confidence-boosting victory.