Dame Maggie, who did not attend the ceremony, picked up her award for best supporting actress in a TV miniseries for her role as the Countess of Grantham in Downton Abbey.
Homeland won the Golden Globe for best TV drama series for the second year in a row, while its British star Damian received the TV drama actor Globe. "I'd like to dedicate this to my mum, looking down on me bursting with pride telling everyone around her how well her son is doing in acting," he said.
Damian's co-star Claire Danes picked up the TV drama actress award and paid tribute to her baby son.
Alex Ganza, executive producer of Homeland, recalled an arduous night of filming where Claire, eight months pregnant, had to do multiple takes being chased in a drainage pipe. "We fairly killed ourselves trying to live up to the hype of that first season and this award tells that maybe, maybe, we didn't screw it up," he said.
There were also awards for Girls as best comedy and show creator Lena Dunham as best comic actress. "This award is for everyone who felt like there wasn't a space for her," an emotional Lena said. "This show has made a space for me."
Don Cheadle was named best comedy actor for his role as Marty Kaan, leader of a team of slippery management consultants in House Of Lies.
Game Change - HBO's account of the rise of Sarah Palin during the 2008 presidential campaign - was named best TV movie or miniseries. Julianne Moore won as best actress in a miniseries or movie for her portrayal of Palin, while Ed Harris - who portrayed presidential candidate John McCain - was the supporting actor winner.
Julianne thanked Tina Fey, the Golden Globes co-host whose Palin skits on Saturday Night Live enlivened the 2008 campaign, and newswoman Katie Couric, who had a contentious interview with Palin that year. She did not thank Palin.
Kevin Costner won the Globe for best acting in a TV miniseries or movie for Hatfields and McCoys.