READ NOTES AFTER FIGHT Timothy vs Vegeta next
The reason Epn won was mainly because of his speed and his transformation. Although both were Stamina types Epn had a bit more speed and his transformation made his power Keep rising as Broly says in the first movie. The only down side to that was that he had to let out his energy that was overflowing, and that is when the beam struggle became Epn's ticket to the 1v1v1 round