Alice in Chains' sixth LP is the band's second set to lead all three lists.
The set starts with 31,000 equivalent album units earned (29,000 in traditional album sales), according to Nielsen Music.
Rainier marks the second set that Alice in Chains has taken to the top of the three charts, following The Devil Put Dinosaurs Here in 2013.
Concurrently, the new album, Alice in Chains' sixth full-length, and third since the death of original frontman Layne Staley in 2002, bows at No. 12 on the all-genre Billboard 200 chart.
After lead Fog single "The One You Know" peaked at No. 9 on the Mainstream Rock Songs airplay chart in July, marking the band's 17th top 10, follow-up "Never Fade" debuts at No. 25.
The bow is Alice in Chains' best since "Get Born Again," which started at No. 17 and reached No. 4 in 1999.