A handful of Republicans joined Democrats to allow the measure to move forward, reflecting concerns in both parties about the administration's strategy.
Republicans praised what they characterized as a narrow and well-executed plan, while Democrats expressed alarm, warning that the mission was vaguely defined.
The passage of the bill was a triumph for Democrats, who drew substantial Republican backing. But it has no path forward, and an election-year compromise is a long shot.
Democrats demanded information from seven top U.S. oil companies about any meetings with the Trump administration regarding plans to control Venezuela's oil industry.