Sprinter Philip took the title in 7.06 seconds after Muir had stormed to victory in a championship record time of eight minutes 35.67 seconds on Sunday, following Saturday's 1500m victory in Belgrade.
The victories were Muir's first two major titles and Philip, who won bronze in the 4x100m relay at the Olympics last year, added to the British medal haul in Serbia.
Team-mate Eilish McColgan claimed third as Muir won by over eight seconds ahead of Turkey's Yasemin Can.
Muir and Can broke away early before the Scot powered away with 300 metres to go and overcame tiredness to win easily.
Muir said: "I was still awake at 3am. I got to bed quite early but just couldn't sleep because I was buzzing from the race yesterday. The legs felt okay but definitely quite tired and I got about five or six hours' sleep.
"Halfway through the race I was thinking 'I'm feeling a bit tired', and I was hoping she wasn't going to ramp it up anymore. I managed to hang in there and knew I had the kick, so I just waited and then I went for it.
"I don't know about that (whether her run was of a similar style to Mo Farah). I think he can run a bit quicker than me. I just knew that's where my strengths lie.
"I knew what Can would likely do being an endurance athlete so I needed to kick as much as I could."
And Muir, who will return to her studies as a vet on Tuesday, knows her double will put further pressure on her to succeed.
She said: "You can't go winning medals and breaking records and not go raising expectations.
"I'll take it all in my stride. I take it as support, not pressure, and I've shown I can deal with it."
Philip ran a British record and personal best, and the 26-year-old wants to improve after her first major senior individual title.
"I crossed the line and overheard my name but you don't believe it until you see it. I came here for the win and I got that," said Philip, who took the British gold medal haul to five in Serbia.
"I've been so calm and I've had the confidence in myself to say 'yes I can do it'. I didn't have any nerves as I usually do. The whole week me and my coach were going over it.
"I feel like this is my year. I've had my injuries but I feel this is the time I can progress."
Lorraine Ugen took silver in the women's long jump, Shelayna Oskan-Clarke also claimed silver in the women's 800 metres and Robbie Grabarz took silver in the men's high jump.
Oskan-Clarke said: "It was close on the line, but my legs were dying and I just didn't have that extra bit. But I tried and I am still happy with a silver."
The women's 4x400 metre relay squad of Eilidh Doyle, Laviai Nielsen, Philippa Lowe and Mary Iheke also claimed silver in three minutes 31.05 seconds behind Poland.
The quartet tried to lead from the start but were caught by Poland on the third leg.
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