Muir crossed the line in four minutes 03.40 seconds at the Atakoy Arena to move ahead of Colin Jackson and Jason Gardener as Britain’s most successful athlete in the competition’s history.
The 29-year-old finished ahead of Romania's Claudia Bobecea and Sofia Ennaoui of Poland, who took silver and bronze respectively.
GB teammate Katie Snowden finished fifth with Ellie Barker 11th.
Having won the 1500m and 3000m double in 2017 and 2019, Muir started as clear favourite but started behind Bobecea at the back of the field before storming into the lead on the final lap.
"I didn't really know what to expect and all my race plans went out the window when it went off that fast," the Olympic silver medalist told the BBC.
"You have to be adaptable in the 1500m and it worked out in the end. I'm in a place now where I'm experienced and I can deal with different things. I'm just so happy.
"Going into this championship I was quite nervous because I didn't think I was at my absolute best... I hoped with grit and determination I would still be able to come here and win.
"As you get older you appreciate these opportunities," she added.
