The Bluebirds striker grabbed what proved to be the winner against La Liga opposition at the Cardiff City Stadium.
Peter Whittingham was also on target for the Welsh outfit as they ensured that they will head into a debut Premier League campaign on a high.
Two goals either side of half-time did the job for Malky Mackay's hosts, as they made the most of the opportunities which came their way.
Whittingham broke the deadlock just before the interval with a spectacular 20-yard volley, after Cardiff had soaked up plenty of early pressure.
They doubled their lead seven minutes into the second period, with Campbell racing clear to confidently round Gorka Iraizoz and slot past a scrambling defence.
Spain international Andoni Iraloa pulled one back for Bilbao on 56 minutes, but Cardiff held on to claim the spoils.
Mackay - who handed Steven Caulker his full debut and saw Aron Gunnarsson make a welcome return from injury - revealed after the game that a deal to bring Gary Medel into his squad from Sevilla is '95 per cent' done.