A Head Full Of Dreams had previously only peaked at number two - held off by Adele at the end of last year.
But their sales surged this week after the band's widely praised performance at the Super Bowl.
They took the the stage alongside Beyonce, Mark Ronson and Bruno Mars, performing to a television audience of around 112 million.
Their chart position this week means every one of the band's seven albums has now reached number one.
Adele's 25 remains at number two whilst last week's chart topper - the David Bowie hits collection Best Of Bowie - slides to third place.
Bowie also takes the number five slot with his most recently released album Blackstar.
Elton John is this week's highest new entry with Wonderful Crazy Night - giving him the 31st top 10 album of his career.
Meanwhile, Danish quartet Lukas Graham have topped the official singles chart with 7 Years.
They're the first Danish act to top the charts since Aqua in 1998.
The band have knocked last week's no. 1 - Zayn Malik's Pillowtalk - down to number two.
Lukas Graham's debut UK release climbed five places to claim the top spot, racking up combined weekly sales of 105,000, including 3.65 million streams.
That means around a third of the band's sales came from streaming - where 100 streams are equal to one physical or download purchase.
Rounding off this week's Top 5 are Jonas Blue & Dakota's Fast Car - a rework of the Tracy Chapman hit - Rihanna's Work, and Shawn Mendes' Stitches.