The broadcaster took home gongs for standalone production and documentary series.
The RTS described Between Life and Death, which won the Single Documentary category, as a "powerful and sensitively filmed portrayal of the most tragic human condition".
"The production team had secured astonishing personal access which they handled with great care and respect, delivering a subtle, moving and beautifully shot documentary," said a release from the society.
The documentary was produced by BBC Productions/BBC Wales for BBC One, filmed over six months in a leading brain injury unit. The programme beat Channel 4's My Big Fat Gypsy Wedding and More4's The Dancing Boys of Afghanistan, to win the category.
The BBC also won the Documentary Series category for its three-part series Welcome to Lagos, produced by KEO north for BBC Two. The programme was praised for "changing the way you see the world".
"The incredible access to this hidden community must have been hard to achieve and was clearly built on trust. It created an eye-opening, refreshing and unsentimental portrait of life in the slums that was a brilliantly compelling watch," the RTS release says.
A third BBC documentary also received recognition in the awards, with BBC Northern Ireland's Breaking The Silence taking the prize for the Nations and Regions Programme category.
According to a release from the BBC, the documentary looked at the issue of suicide, speaking to families in Co Armagh and Co Tyrone who had lost their relatives.
"Breaking The Silence was a deeply moving and important documentary showing how suicide can affect anyone," said Deirdre Devlin, executive producer of the documentary.
"We're incredibly grateful to the Royal Television Society for recognising the programme in this way and I would like to extend that gratitude to the contributors to this documentary who demonstrated great courage, conviction and kindness in sharing their painful stories with us."
Free daily newsletter
If you like our news and feature articles, you can sign up to receive our free daily (Mon-Fri) email newsletter (mobile friendly).
