Amazon.com Inc. on Monday put itself in the unusual position of being a first-mover on price cuts when it slashed the sticker price on more than 100 items at Whole Foods Market Inc., many by more than 30%.

Amazon typically relies on algorithms that scrape competitors’ prices before automatically matching or narrowly undercutting them on its website. It focuses on items that are most popular on the site and that drive traffic, according to former executives in Amazon’s retail divisions. That gives the retail giant a reputation...