The measure failed on a vote of 51-to-49 in the Republican-led chamber.
Republican leaders were seeking to overturn the Interior Department rule under the Congressional Review Act.
President Barack Obama finalized a rule in November that would force energy companies to capture methane that's burned off or "flared" at drilling sites because it earns less money than oil.
Democrats and environmental groups say the rule protects the public health and generates millions in revenue for state, local and tribal governments.