The boy band, which was not in attendance, was feted as Best British Group at London's Wembley Arena ceremony, while Drag Me Down earned the stars the Friday Download Best British Single title.
Taking to Twitter.com after the event, singer Niall Horan posted, "Wow just found out we won 2 teen awards today .. Thank you to all of your for voting and @BBCR1 for the support".
Sheeran, another absent winner, took home the Best British Solo honour and sent fans a message of thanks in the form of a pre-recorded video.
Other big prizes of the night included Best British TV Show, which went to The X Factor, and Best Film, which was awarded to The Hunger Games: Mockingjay - Part 2.
The Radio 1 Teen Awards were hosted by DJ Nick Grimshaw, alongside Demi Lovato, Rita Ora, The Vamps and Troye Sivan, and featured a surprise appearance by Justin Bieber, who kicked off the event with a medley of his hits What Do You Mean?, Where Are U Now and Boyfriend. Little Mix, Nick Jonas, 5 Seconds of Summer, All Time Low and Lovato also hit the stage during the prizegiving.