The 33-year-old star played Lisa Lynch, who died in 2013 at that same age after suffering from cancer, in the one-off drama.
Ms Lynch started an irreverent blog after learning about her diagnosis, when she was just 28 and trying to get pregnant.
Gavin And Stacey actress Smith, who became close to Ms Lynch and previously portrayed Cilla Black on screen, tweeted as the Sunday night drama began: “ Emotional. So overwhelmed by your amazing support. Thank you. Love you all! I know she’ll be watching with us.”
The C-Word was a huge hit with viewers.
Peter Gibbons wrote on Twitter: “ I’m in bits watching this. Sheridan Smith is a phenomenon.”
Broadcaster Fearne Cotton said: “Thank you, Lisa Lynch, for telling your story. The C-Word was the most important bit of TV as you continue to help so many.”
Vivien Taylor Ken Adams wrote: “ Watched The C-Word... Speechless...”
Tracey Preddy added: “I never tweet, but The C-Word was the most accomplished drama I have ever watched, congratulations.”
SineadsTweets wrote: “Phenomenal performance already. Sitting here in tears. Far too real.”
Ms Lynch’s brother James D McFarlane wrote: “ If her book and this production get more people checking for lumps, and talking about cancer, then Lisa Lynch and The C-Word will have succeeded.”
The C-Word averaged 3.8 million viewers, peaking at 4.2 million, and a 17.4% share of the audience, beating all other channels apart from ITV, which broadcast Sunday Night At The Palladium.