The programme, based on Sally Rooney's book of the same name, starred Paul and Daisy Edgar-Jones as two lovestruck teenagers, and became a massive hit across the globe.
Picking up his honour at the virtual awards, Paul thanked director Lenny Abrahamson - who won the Best Director - Drama gong - and praised Daisy as "one of the most incredible actresses working in our industry."
"Normal People" also took home the Best Drama prize, as well as Best Supporting Actor and Actress gongs for Fionn O'Shea and Sarah Greene respectively. In total, the programme won nine of the 15 gongs it was up for - including cinematography, production design and the Script Drama prize for Rooney.
Accepting the prize, Nicola gushed, "I'm really shocked - oh my god I'm so shocked. Hearing Luke Skywalker say my name is such a shock! I'm so proud to be an Irish actor, I'm so proud to be so proud of that!"
"This is so special because all you really want is people at home to be happy with what you are doing. I was at the BAFTAs when Paul (Mescal) won and it felt like a win for everybody. So to be recognised at home is really so special, it's so amazing and I am so grateful, thank you so much."
Gabriel Byrne was named Best Actor - Film for his role in "Death of a Ladies Man", and accepted the gong from "The Crown" star Olivia Colman as he said, "Well that's a real shock to me, thank you - and I'm not just saying that. (The other nominees are) all great actors and I'm honoured to be among them."
Winners of the 2021 IFTA Film & Drama Awards are: