Light Yagami ensures his continued dominance and influence over the Death Note's power by outsmarting his opponents, maintaining secrecy about his identity as Kira, manipulating others to do his bidding, and constantly evolving his plans to stay one step ahead of those who seek to stop him, such as L and Near. His strategic thinking, intelligence, and willingness to use any means necessary to achieve his goals allow him to maintain control over the Death Note's power throughout the series.