Roadkill, which dramatically tells the story of a trafficked child, received six nominations and won two.
Mercy Ojelade's powerful depiction of the play's central character Mary won her the top honour in the best female performance category for the Ankur Productions and Pachamama Productions play.
Catherine Wheels, the children's theatre specialists, also triumphed at this year's awards, picking up three of the ten awards available for their production of White.
Now in their ninth year, this year's CATS ceremony was held at Edinburgh's Festival theatre and presented by actress Clare Grogan.
CATS co-convener and theatre critic for The Scotsman Joyce McMillan, said: "Roadkill is a show that achieves the highest artistic standards in every area, from writing, acting and directing to design, sound and technical co-ordination."
She added: "Even more importantly, though, it draws that artistic energy from the company's passion for its subject, and from their shared determination to make us aware of the scandal and tragedy of people-trafficking in our time - not as some distant problem in faraway places, but as something that is happening now, in the very fabric of our own cities, and perhaps even in the flat next door."
Andy Manley, creator of White for Catherine Wheels, said: "Winning Best Production for Children is brilliant. I have a godson who is two-and-a-half and when I was talking about making the show his obsession with colour was paramount all along.
"He just wanted to name colours and own them, so was very important in the middle of it."
The Best Male Actor award went to David Birrell, for his performance in the title role in Sweeney Todd at Dundee Rep.
He beat off competition from Alex Ferns in Scottish Theatres Consortium touring production of The Hard Man and Peter Forbes in the Royal Lyceum's production of Educating Agnes.
The Best Director award went to Muriel Romanes, for her creation of Linda Griffiths' Age of Arousal for Stellar Quines Theatre Company and the Royal Lyceum. The award for Best Music and Sound was shared between Dundee Rep's production of Stephen Sondheim's musical Sweeney Todd, under musical direction of Hilary Brooks and the National Theatre of Scotland's production of David Greig's The Strange Undoing of Prudencia Hart, with original music by Alasdair Macrae.
Announcing the award, Robert Dawson Scott of STV said: "How do you separate the challenge that Hilary Brooks had at Dundee, faced with one of the most demanding scores in all musical theatre, from the challenge of writing new music and combining that with much-loved existing music to make something as wittily brilliant and contextually clever as Alasdair Macrae managed for Prudencia Hart?
"They were both tremendous achievements and we have decided the Best Music And Sound category should be shared."
Best male: David Birrell, Sweeney Todd: The Demon Barber of Fleet Street, Dundee Rep Theatre.
Best Female: Mercy Ojelade, Roadkill, Ankur Productions/Pachamama Productions.
Best production: Cora Bissett, below, Roadkill.
Best Ensemble: The Three Musketeers And The Princess of Spain, Traverse Theatre Company/Belgrade Theatre, Coventry/English Touring Theatre.
Best Director: Muriel Romanes, Age Of Arousal, Stellar Quines Theatre Company/Royal Lyceum Theatre Company.
Best Design: Shona Reppe (set and costumes) and Craig Fleming (lighting), White, Catherine Wheels Theatre Company.
Best Music and Sound: Joint winners: Hilary Brooks, Sweeney Todd, Alasdair Macrae, The Strange Undoing Of Prudencia Hart, National Theatre of Scotland.
Best Technical Presentation: White.
Best Production for Children and Young People: White.