DALLAS  Exxon Mobil’s chairman and chief executive, Rex W. Tillerson, defeated a shareholder effort on Wednesday to take away one of his jobs at an annual meeting punctuated by a debate of the company’s policy toward renewable energy and global warming.

The vote was nonbinding and would not have guaranteed a change in company policies had it passed. But by defeating the challenge, which was supported this year by many members of the Rockefeller family, Mr. Tillerson avoided a serious rebuke to his authority to run the world’s largest independent oil company.

The resolution to divide the top two positions won 39.5 percent of the vote, about the same as last year.

The vote was announced after a robust debate among shareholders, those who defended management as a great engine for profits and those who argued that a narrow focus on developing oil and gas as energy sources would threaten the global environment and ultimately the company’s financial health.