The actor - who played suspect Terry Boyle in the BBC police drama - joined co-stars including Martin Compston on stage at the ceremony to accept the award for Returning Drama.
Jessop, 36, swung his hips on stage as the audience applauded the show's victory and then pulled a series of poses on stage to rapturous cheers.
Compston said backstage: "Thank you to everyone who voted for us. Tommy was fantastic. I think he’s going to take the award!"
Jessop - who joined the cast of Line Of Duty in 2019 - has Down’s Syndrome. He had his breakthrough tole in 2007 starring opposite Nicholas Hoult in BBC drama Coming Down The Mountain.
The best New Drama award went to Channel 4 drama It's A Sin about the lives of young gay men living in London in the midst of the AIDS/HIV crisis of the 1980s.
Though the show has been highly critically acclaimed the pair were visibly shocked to have been voted the winners of an NTA by the viewing public, beating hit Netflix costume drama Bridgerton.
Davies admitted on stage: "That's a surprise - thank you so much!"
Alexander said: "Making this show was the hugest privilege of my life."
Davies also added: "This was a show about a global pandemic in which many people lost their lives. So it is nice to be able to dedicate this to those we lost, those who learnt, those who lived, and those we loved."
Watch: Why Piers Morgan REALLY wants to win at the NTAs