The bill marks the ninth attempt by the House to secure pipeline approval. Republicans hope the timing will give Louisiana Republican Rep. Bill Cassidy an edge over Sen. Mary Landrieu in a runoff race.
The Senate, at Landrieu's urging, plans to vote next week. The White House says it takes a "dim view" of being forced to make a decision it has said would be based on whether the pipeline worsens global warming.
The votes offer a preview of what is to come on energy and environmental issues when Republicans take over the Senate next year, solidifying their control of Congress.