The show has 14 nominations for the main awards and the Bafta TV Craft Awards, which were announced together.
Hugh Grant's drama A Very English Scandal is next with 12.
Bodyguard's Keeley Hawes will go up against Comer and Oh for best actress - but there was no room on the best actor list for her co-star Richard Madden.
That's a big surprise given that he won the Golden Globe for best actor in a TV drama in January.
Bafta bends the rules for Killing Eve
The kooky spy drama's other acting nominees are Fiona Shaw, who played spymaster Carolyn, and Kim Bodina, who was Villanelle's handler Konstantin. They are up for best supporting actress and best supporting actor respectively.
And Phoebe Waller-Bridge is nominated for best drama writer.
But its nominations were only possible because Bafta bent its own eligibility rules, which say shows "must have had the worldwide premiere transmission in the UK".
Killing Eve premiered in the US on BBC America five months before it arrived on BBC One.
A Bafta spokeswoman said: "Bafta's TV committee has deemed Killing Eve eligible owing to the significant creative contribution from key talent residing in the UK both in front of, and behind, the camera. Development and post-production also took place in the UK."
Bodyguard and Killing Eve are both up for best drama series, alongside BBC One's Informer and Sky Atlantic's Save Me.
Hawes is in the running for two trophies after also receiving a best supporting actress nomination for Mrs Wilson.
Hugh vs Benedict
Grant is among the nominees for best actor for playing disgraced Liberal leader Jeremy Thorpe in A Very English Scandal. His co-star Ben Whishaw is up for best supporting actor.
Grant's rivals for best actor are Benedict Cumberbatch for Patrick Melrose, Chance Perdomo for Killed By My Debt and Lucian Msamati for Kiri.
Bafta chairwoman Dame Pippa Harris told the Press Association some "difficult" decisions had been made because there were only four spots up for grabs on each shortlist.
She said: "When you look at those four performances, it's very difficult to say 'Well, which one you would pull out in order to put Richard Madden in there?"'
The top Bafta TV nominees
- Killing Eve - 14
- A Very English Scandal - 12
- Patrick Melrose - 6
- Bodyguard - 5
- The Little Drummer Girl - 5
- Mrs Wilson - 4
- Mum - 4
Who's up for the comedy awards?
This Country star Daisy May Cooper is in with a shot of winning the best female comedy performance award for the second year in a row.
But she'll face stiff competition from Jessica Hynes for There She Goes, Julia Davis for Sally4Ever and Lesley Manville for Mum.
Sally4Ever and Mum are also up for best scripted comedy, alongside Derry Girls and Stath Lets Flats - both Channel 4 shows.
But the Car Share finale didn't make it on to the list, with Peter Kay and Sian Gibson also missing out in the comedy performance categories.
However, they are up for best comedy writing and the show is up for the must-see moment prize, which will be voted for by the public.
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