An expression that implies utter defeat with ease is "wipe the floor with".
Before the competition you can say "I will wipe the floor with [insert name or pronoun]".
After the competition you can say "I wiped the floor with [insert name or pronoun]".
All of those three imply some degree of defeat, but not necessarily humiliation. The strongest is "to take someone down a peg" but this sounds more like genteel British understatement than any kind of sincere gloating.
Instead, on the polite side, try "rub someone's nose in the dirt", implying that someone was so defeated they were forced face-first into ...