Triumphs over is a phrase that implies success in overcoming a challenge or obstacle. The crossword solutions for this term are BEATS, BESTS, and DEFEATS. BEATS implies a physical victory, such as in a boxing match. BESTS implies a mental victory, such as in a game of chess. DEFEATS implies a general victory, such as in a competition. All three words imply a successful outcome in which one party has triumphed over the other.