The show, which sees players "murder" each other in a Scottish castle, developed a cult following after it launched in November.
Derry Girls and Bad Sisters won the top TV prizes, while Ben Whishaw and Kate Winslet were among the acting winners.
But Winkleman's other series Strictly Come Dancing lost out to The Masked Singer for best entertainment show.
The ceremony, which was hosted by comedians Rob Beckett and Romesh Ranganathan, took place on Sunday at London's Royal Festival Hall.
Accepting the prize for best reality series on behalf of The Traitors, Winkleman recalled the meeting she had with commissioners ahead of its launch.
"I went, 'OK, just to be clear, we're going to Scotland, we've got some cloaks, we're going to use the word murder, I've got a big rollneck and I'm holding a ceremonial pouch, are you OK with that?' And they went 'go for it'."
She took the opportunity to ask her husband from the stage: "Please, can we have a dog?"
Other winners included a documentary about Sir Mo Farah which revealed the athlete had been illegally trafficked to the UK as a child.
A special edition of The Repair Shop which featured King Charles was named best daytime programme.
Presenter Jay Blades said it was the "first time" that a "six-foot black guy, from Hackney, gold tooth, single parent" had been presented with an award for daytime TV.
Asked about Richard Osman's suggestion that the daytime category should be expanded to include more programmes, Blades told BBC News: "If Bafta can do that, it'd be brilliant, but it's above my pay grade!"
Winslet won best leading actress for her performance in I Am Ruth, about a mother who tries to help her depressed teenage daughter.
The star, who acted opposite her daughter in the series, said "small British television dramas can be mighty" and mental health stories such as this one "need to be heard".
She added: "If I could break it in half, I would give the other half to my daughter Mia Threapleton, we did this together, kiddo."
Winslet held off competition from Sarah Lancashire, who was nominated for her performance in HBO's Julia. The most recent series of her hit police drama Happy Valley was broadcast too late to be eligible this year.
Sharon Horgan, whose Apple TV series Bad Sisters won best drama, used part of her acceptance speech to say she stands in "solidarity" with the current writers' strike taking place in the US.
Derry Girls was named best scripted comedy programme following its conclusion last year. "What an amazing end to our Derry Girls journey," said its writer Lisa McGee.
She recalled how the show had been a hard sell in the early days because it "didn't have runaway hit written all over it, but what we found is in the specific there is always the universal".
The show's star Siobhan McSweeney won best female comedy performance for her performance as Sister Michael in Channel 4 comedy Derry Girls.
She joked: "As my mother lay dying in Cork, one of the very last things she said to me was, would I not consider retraining as a teacher?
"If she could see me now getting a Bafta for playing a teacher... joke's on you."
James Bond and Paddington star Whishaw collected best leading actor for his performance as an under-pressure doctor in BBC series This Is Going To Hurt, based on the best-selling memoir.
On stage, the 42-year-old actor said "everybody in the show is just mind-blowing" and "most of all thank you, Adam Kay, for writing this wonderful role".
However, the medical programme lost out on best mini-series to BBC Three's Mood, one of the night's most surprising winners.
Sir Mo Farah won the single documentary prize for The Real Mo Farah, which revealed the Olympic gold medallist had been illegally trafficked to the UK as a child.
Dedicating the award to "children who are being trafficked", Sir Mo said: "The kids have no say at all, they are just kids and no child should ever go through what I did, I hope my story shows they aren't alone, we are in it together."
The in memoriam section paid tribute to TV stars who have died in the past year, including talk show host Jerry Springer, Strictly Come Dancing judge Len Goodman, presenter and drag queen Paul O'Grady, Doctor Who actor Bernard Cribbins and Dame Edna Everage star Barry Humphries.
The Masked Singer beat Ant And Dec's Saturday Night Takeaway and Strictly Come Dancing to win best entertainment programme.
Host Joel Dommett said he was surprised to win, describing the show as "so silly and so wonderful... it has brightened up so many families and homes".
Judge Mo Gilligan added: "People tried to mock it when it first came out, and now it has won a Bafta. It is great escapism... people at home don't want to watch something depressing."
Joe Lycett vs Beckham: Got Your Back At Xmas - which saw the comedian criticise the former footballer for his links with Qatar - won the features category.
The comedian dedicated his Bafta to the "people still being oppressed in Qatar".
Lenny Rush, the 14-year-old actor who starred opposite Daisy May Cooper in Am I Being Unreasonable?, said he was "over the moon" to win best male performance in a comedy programme.
The memorable moment award went to Paddington bear having tea with the late Queen during the Platinum Jubilee: Party At The Palace celebrations.
Winkleman also won best entertainment performance, commenting that she did not want to get emotional because her eyeliner would run.
She also thanked her mother and father and said the award was "for you" before joking: "You can't have it, but you can touch it."
Lewis Capaldi and Jax Jones performed at the ceremony and followed last month's Bafta TV Craft Awards, which saw This is Going to Hurt and House of the Dragon take home three prizes each.