Sara Paulson is compelling on American Crime Story. She does her part with depth and with subtle details. She deserved to win because she makes her character believable as well as true to the facts of the case. She is talented and the voting audience took notice and recognized her efforts.
Yes, Sara Paulson deserved to win Outstanding Lead Actress because she is exactly what the award says she is: an outstanding lead actress in a TV show. She deserved to win any award she was nominated for based on her ability to act. She will win many more in the future.
Yes, Sara Paulson deserved to win the Emmy for Outstanding Lead Actress for her portrayal of Marcia Clark in The People Vs. OJ Simpson: An American Crime Story. She played the role beautifully, capturing a vulnerability that was not apparent to the public when the actual trial was happening. She was up against a group of excellent actresses who all would've been deserving if they'd won this award.
Indeed, she missed out on wins the previous four years for her performances on Game Change and American Horror Story, each of which deserved to win in their own right. Another argument supporting Sara's win is that playing a real person is kind of a challenge. Marcia Clark is really well protrayed. So, Sara deserves the win.