The 37-year-old Glaswegian plays crooked Lydia Rodarte-Quayle in the hit drama and was honoured as the show scooped the top prize for Drama Series Cast.
As awards season hots up, with the Oscars on the horizon, Matthew McConaughey was again a winner in the Best Actor category for Dallas Buyers Club - following up his success at the Golden Globes and Critics Choice Awards.
Cate Blanchett also continued her winning streak, taking Best Actress for Blue Jasmine.
Dames Helen Mirren and Maggie Smith struck a blow for Britain.
Dame Helen scooped the gong for Best Actress in a movie or mini-series for her performance in the biopic Phil Spector, and Downton Abbey's Dame Maggie won the accolade for Best Actress in a drama series.
The main event saw David O Russell's American Hustle win the top honour, the award for outstanding cast, beating 12 Years A Slave, Dallas Buyers Club, August: Osage County and Lee Daniels' The Butler.