Twitter Inc.’s shares soared more than 15% after the social-media company Thursday said it was doing a better job of extracting more revenue from people using the service, even as its number of engaged users shrank again in the third quarter as it continued to purge fake accounts.

Twitter said its number of monthly active users world-wide, the metric most closely watched by Wall Street for years, fell by nine million from the second quarter to 326 million—its steepest decline ever and more than it had anticipated. The previous...