Both sides pressed the ball in the opening stages, with Bilbao making four changes to the side that faced Schalke in the Europa League on Thursday.
Messi so nearly found the corner with a free kick after 24 minutes, before Jon Aurtenetxe cleared a Pique header off the line moments later.
Barcelona continued to attack in the latter stages of the opening period, and they found the opener five minutes before the break when Iniesta collected a Messi pass before firing home.
Bilbao entered the second period with a better purpose, but it was Barcelona who continued to look the more dangerous and Tello brought a fine save out of Iraizoz after 55 minutes.
Barcelona moved 2-0 ahead just before the hour mark when Messi converted from the spot after Tello had been felled by Javi Martinez in the area.
Chances were few and far between in the latter stages, as the home side closed out the comfortable win.