The "Not Fair" singer's third record toppled Paolo Nutini's three-week reign with Caustic Love to take the top spot.
The Official Charts Company confirmed that Sheezus was eligible despite a flash sale promotion for 99p on Google Play early last week.
But Rhys Webb of The Horrors, who also have a new album out, criticised Allen's aggressive marketing tactics.
"Her record company have done that to give Lily a surefire number one," he told the Daily Star. "Albums should be something that are there for a lifetime."
Take That's greatest hits compilation Never Forget also re-entered the chart at number 21, eight years after its initial release.
Paloma Faith's A Perfect Contradiction and Black Stone Cherry's new Magic Mountain completed the top five at numbers four and five respectively.