The e-commerce giant plans to introduce a new competition show next month in which entrepreneurs pitch their products to a studio audience as well as to judges including Amazon executives and celebrities like Goop founder Gwyneth Paltrow and designer Christian Siriano. Finalists will have their inventions sold in a new Amazon “Buy It Now” online store, and the winner of each episode will earn $20,000.

The show is the retailer’s latest attempt to marry content and commerce. Persuading consumers to shop through Internet-enabled televisions has long been a goal of traditional entertainment companies, but getting viewers to scan the QR code can be difficult.

By creating shows that highlight its sellers and their products, Amazon has a better shot at getting viewers to shop—especially younger audiences who are already doing this on apps like TikTok, said Bernstein analyst Mark Shmulik.

“This feels more elegant than QR codes,” Shmulik said of Amazon’s new game show.

Over the past few years, Amazon has introduced ads with QR codes in about 100 shows and movies, including “The Summer I Turned Pretty,” “The Boys” and, more recently, NFL football games.

Its previous attempts at creating shows that tie in commerce have been hit or miss. In 2017, after less than a year, Amazon canceled its QVC-like show, “Style Code Live,” featuring experts sharing fashion tips and promoting products that the audience could buy.

Other shows that use a competition format, like “Making the Cut,” featuring rival fashion designers and hosted by Heidi Klum and Tim Gunn, lasted three seasons. In that show, the winners could create a co-brand with Amazon Fashion and launch their existing lines in that store.

The “Buy It Now” panel of rotating judges includes Ring creator Jamie Siminoff, whose smart-doorbell company Amazon acquired in 2018, and four other Amazon executives, including Tanner Elton, vice president for U.S. ad sales. The company decided to use Amazon executives as judges to give the audience a better sense of how it works with smaller retailers, said Lauren Anderson, head of brand and content innovation for Amazon MGM Solutions.

“It felt like a regular meeting at Amazon,” Michelle Rothman, vice president of shopping for Prime Video, said of her experience judging on the show.

In each episode of the show, which is scheduled to debut Oct. 30 and is hosted by comedian J.B. Smoove of “Curb Your Enthusiasm,” entrepreneurs have 90 seconds to pitch their invention to a studio audience. The audience votes on whether the product should go to the judges panel that includes former skateboarder Tony Hawk, “Black-ish” star Anthony Anderson and actress Tabitha Brown.

Part of Amazon’s goal with the show is to help smaller retailers gain broader exposure on the e-commerce site.

Kiri Masters, the former head of retail-marketplace strategy at Acadia, a digital marketing firm that works with midsize advertisers, said it has become increasingly expensive for small businesses to earn top billing in search results on Amazon through paid ads because of heightened competition to get those top spots.

Winners get support in determining how to describe their products to attract customer attention on the “Buy It Now” store. Such help is very valuable to entrepreneurs like Felicia Jackson, chief executive of CPR Wrap, a device that makes it easier for people to perform CPR, and a contestant on the show.

“We don’t just want to sell locally or nationally, we want to go international,” she said, noting that just being on the show has helped her improve the visibility of her products. “I literally prayed for something like this to happen.”

Write to Jessica Toonkel at jessica.toonkel@wsj.com