It was a scrappy start to the match with both sides struggling to find possession in the early stages.
Shortly after the restart Osasuna had another glorious opportunity, as Sola found space in the box but was stopped from scoring only by a timely Aymeric Laporte tackle.
Armenteros then put a header straight at Iraizoz, before Osasuna were made to pay for spurning so many chances.
In the 63rd minute, Markel Susaeta hammered in an Ibai Gomez pass to give Bilbao an unlikely lead.
Fernando Llorente should have made it 2-0 with 10 minutes left but blazed a header over the bar.
It did not matter in the end as Bilbao escaped with three vital points.