The way I see it, is that the P-51 beat the Bf 109 on its own game. They were very similar fighters in the sense that their main strength laid in their speed and power instead of sheer manoeuvrability. The Bf 109 dominated every fighter in these power fights, 'in the vertical'. But then when fighters like the P-51 or to a lesser extent P-38 and P-47 came along, they outclassed the Bf 109. And I am saying that as a Bf 109 enthusiast. I agree with Njaco, that the later Bf 109 was on par with the P-51 but in 1944 the Bf 109G-6 was definitely outclassed until the G-10 and K-4 appeared at the end of 1944.
The P-51 was not the super-fighter it is often mistaken for. But it was the fastest fighter around, at all altitudes. It rolled well, handled well, dived very well, had decent armour, effective armament, ... However, except for speed and range, it was not superior in any sense! But, compared to the standard Bf 109G or Fw 190A, it beat them at the most important element in air combat: initiative! Due to its superior speed it could break off any fight and engage it at will. This was what the German fighters always had over their opponents. Now, the roles had been turned. Also, German fighters were now forced to press on with the attack on the bombers, making the German fighters a prey for the P-51s.
And couple that with the best trained pilots in the world ...
Kris