Previous to this we learned that Mat's father was incredibly adept with the quarterstaff, and was the best in the Two Rivers. He was able to beat Tam, and Tam was quite a skilled soldier to have gotten a Heron marked blade (granted it was explained off that he 'bought it', but I don't think any of us really believed that ). Mat probably learned quite a bit from his father, so it stood to reason that Mat was quite capable. Granted, this doesn't explain it all, but it does lead up to Mat winning his match (in my opinion, at least).