Oprah, Meghan and Harry drew a sizable audience on Sunday night, making for an old-style prime-time television moment in the age of on-demand viewing.

Oprah Winfrey’s explosive two-hour interview with Meghan Markle and Prince Harry, who had largely kept their silence after announcing last year that they would give up their duties as members of Britain’s royal family, attracted 17.1 million viewers on CBS, according to preliminary Nielsen figures.

The number of viewers climbed as the show went on. It drew 16.9 million in the first hour and 17.3 in the second, Nielsen reported. That audience was about twice the size of the viewership for the prime-time ratings winner in a given week.

In a time when Netflix and other streaming platforms dominate viewing habits, the ratings for “Oprah With Meghan and Harry: A CBS Primetime Special” were strong — but they did not come close to the figures of similar prime-time exclusives from past decades. And the number of viewers fell short of the 22 million who watched a similarly ballyhooed interview in 2018, a “60 Minutes” episode in which Stephanie Clifford (also known as Stormy Daniels) told Anderson Cooper about her past affair with Donald J. Trump.

Ms. Winfrey’s special aired after days of anticipatory coverage hinting at what the couple might reveal about their experiences with the royal family and their decision to leave the palace behind.

Meghan did not hold back during the interview, telling Ms. Winfrey that she had contemplated suicide while living as a royal. She also blamed Britain’s first family for not providing her with sufficient protection from Britain’s ferocious tabloid press and described racism within the royal family, saying that, during her pregnancy, there had been “concerns and conversations about how dark” the skin of her child would be. Harry revealed a strained relationship with his father, Prince Charles, and brother, Prince William.

The high level of interest in a special on a big broadcast network was something of a throwback to a moment when prime-time television interviews, jampacked with commercials, became a gathering spot for a mass audience.

The “big get” interview is a TV genre unto itself, in which a famous anchor or host elbows out rivals to land an exclusive sit-down with a newsworthy subject. It is also a genre past its heyday. Along with Diane Sawyer and Barbara Walters, Ms. Winfrey, an interviewer extraordinaire who started her TV career in the 1970s, was a major player when the competition for such shows was at its height.

In 1993, Ms. Winfrey’s prime-time interview of Michael Jackson at his Neverland Ranch, broadcast by ABC, attracted an audience of at least 62 million. Six years later, also on ABC, Ms. Walters sat down with Monica Lewinsky for a two-hour special that drew 48.5 million.

Since then, the rise of digital media and its infinite screen-time options has cut deeply into the might of the big broadcasters. As the viewing audience fractured, opportunities for must-see prime-time interviews became vanishingly rare. Even the biggest one-on-ones of recent years have lacked the drawing power of the specials from two decades ago and more. The audience of 17.1 million for Ms. Winfrey’s interview of Meghan and Harry matched the number of viewers who tuned in when Caitlyn Jenner revealed that she was transgender to Ms. Sawyer on a 2015 episode of ABC’s “20/20.”

The Sunday night special was unusual in that it was not overseen by a network news division. Ms. Winfrey’s company, Harpo Productions, produced it, and CBS paid at least $7 million to license the show, according to a person with knowledge of the arrangement. (The Wall Street Journal previously reported the figure.) The deal was also a gamble: It was taped after the network had bought the rights, according to two people with knowledge of how the show was made. During the interview, Ms. Winfrey said she had been trying to land the exclusive with the couple for about three years.

CBS emerged the winning bidder despite Ms. Winfrey’s rocky experience at “60 Minutes,” where she was a special contributor in 2017 and 2018. In a 2019 interview with The Hollywood Reporter, Ms. Winfrey revealed that the show’s producers had criticized her delivery, saying she had “too much emotion” in her voice, even when she said her own name. (Ms. Winfrey has maintained a connection to the network through her good friend Gayle King, an anchor of “CBS This Morning,” and appeared on that show Monday.)

Further complicating CBS’s attempt to get the big get was the thicket of media companies surrounding Ms. Winfrey and the former royal couple. Ms. Winfrey has her own cable network, OWN, and is a major part of the streaming platform AppleTV+. Recent episodes of Apple’s “The Oprah Conversation” have featured her interviews of Barack Obama, Dolly Parton and Mariah Carey.

Meghan and Harry, for their part, signed a multiyear deal with Netflix last year to make documentaries and other shows. They also signed on to make podcasts for Spotify and released the first installment on Dec. 29. It included guest appearances by Elton John, Tyler Perry and other celebrities, as well as the first public utterance from their son, Archie.

The pact between CBS and Harpo Productions was largely focused on TV rights. The interview ran live on ViacomCBS’s newly rebranded streaming service, Paramount+ but at least for now will not be available on Paramount+ for on-demand viewing. Instead, the special will be available on CBS.com and the CBS app for 30 days, a CBS spokesman said.

Originally slotted for 90 minutes, it ended up a two-hour show. Before the broadcast, CBS released teaser clips, and British tabloids that have been unfriendly to Meghan shot back with anonymously sourced items on her apparent misdeeds.

The estimate of 17.1 million viewers will only grow after Nielsen tabulates some viewers who streamed the special, as well as out-of-home viewing.