The visitors were the first to threaten as Aymeric Laporte rose highest inside the box having lost his marker, but his header went narrowly wide of the right post.
The Spanish outfit came close again just five minutes later when once more Napoli failed to deal with a lofted ball into the box, this time Aritz Aduriz latching on to it to draw a good save from Rafael Cabral.
Bilbao did find the back of the net four minutes before half time, however, as Oscar de Marcos slid a square pass to Iker Muniain, who took a touch inside the box before coolly slotting the ball into the bottom corner.
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The hosts were level with just over 20 minutes remaining in the match courtesy of a fine solo effort from Gonzalo Higuain, who burst between two defenders before firing a low strike into the bottom corner.
Higuain almost turned provider moments later as he played the ball through for Jose Callejon, but the Spaniard put his effort just wide.
Iraizoz was called into action again shortly afterwards, but once again he was up to the challenge, this time denying Higuain with a fine stop as his side held out for the draw.