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The excitement over the new album has also boosted sales of Mr. Timberlake‘s other solo albums, Nielsen Co. said. Last year, “FutureSex/LoveSounds” and 2002’s “Justified” sold 39,000 and 21,000 copies each, but this year they’ve already sold 29,000 and 17,000, respectively.

“As the marketing sort of picks up for the new record and the single goes to radio … you definitely start to see interest,” said David Bakula, Nielsen’s senior vice president of client development and analytics for entertainment.

Mr. Bakula said ‘N Sync sales are up, too.

“20/20” was streamed 7.73 million times on Spotify in its first week, putting it second behind the 8 million streams set by Mumford & Sons’ “Babel” last year. Steve Savoca, Spotify’s head of content, said Mr. Timberlake‘s colossal first-week numbers are another example of how streaming music helps artists sell albums.

Mr. Fallon said Mr. Timberlake worked tirelessly ahead of the five shows and he’s proud of his friend’s success.

Justin was here till 11 o’clock most nights choreographing dance moves so he nailed it the next night,” he said. “And he was sick at the time.”

Mr. Corson said this week’s success could change the expectation of Mr. Timberlake’s follow-up to “20/20,” which will likely be released later this year.

“It sure should,” he said with a laugh. “Part two is now even more anticipated.”

Mr. Timberlake could even show up for a stint with Mr. Fallon again.

“We are already talking about it,” Mr. Fallon said.