Northern Ireland put in a dominant display against Belarus on Saturday but failed to find the breakthrough.
However, once Price tucked away Dion Charles’ pass in the 15th minute it seemed like a weight had been lifted off the players’ shoulders against Bulgaria.
Price, 21, fired home a second and Mitov’s own goal made it three before half time.
Charles saw an effort ruled out after Conor Bradley strayed offside, but Price’s hat-trick strike and a late effort by substitute Magennis rounded out a famous win.
When asked if the superb strike to secure his hat-trick was the best of his career, Price said: “By far, 100%.”
“There’s no better feeling. My mum and dad were here to see it,” the Standard Liege midfielder added.
“All the sacrifices they’ve made to get me to this point, and they can come and witness that, it’s great for me and my family. It’s just surreal.”