General Dominance:
* Controlled
* Ruled
* Governed
* Presided over
* Overpowered
* Subjugated
* Conquered
* Suppressed
* Overwhelmed
In a specific context:
* Outshone (in terms of talent or performance)
* Outweighed (in terms of importance or significance)
* Outnumbered (in terms of quantity)
* Outmaneuvered (in terms of strategy or tactics)
* Overshadowed (in terms of influence or prominence)
Figurative Dominance:
* Prevailed
* Trumped
* Superseded
* Took precedence
The best synonym for "dominated" will depend on the specific context and the nuance you want to convey.