Chevron Corp. shareholders voted for a proposal to reduce emissions from the company’s customers, the latest sign that oil titans are coming under increasing pressure to address environmental concerns.

According to a preliminary tally, 61% of investors backed the proposal at the company’s annual investor meeting on Wednesday, rebuffing the company’s board, which had urged shareholders to reject it. An item asking Chevron to report on how a significant reduction in fossil-fuel demand would affect its business and a request for a report on political lobbying were narrowly voted down.

The vote, which came on the same day Royal Dutch Shell Plc was ordered by a Dutch court to slash its emissions harder and faster than planned, highlights an unprecedented push to hold oil giants accountable for their contributions to climate change. Also on Wednesday, at least two nominees of an activist investment firm won seats on Exxon Mobil Corp.’s board in a major setback for Chief Executive Officer Darren Woods.

Chevron should be able to increase returns to investors at the same time as it strives to […]