WASHINGTON—Congress overturned a rule by an Obama-appointed financial regulator that would have made it easier for consumers to sue banks in groups, with Vice President Mike Pence casting a tiebreaking vote in the Senate.

The 51-50 vote handed the financial industry its most significant legislative victory since President Donald Trump took office and was a rebuke of Consumer Financial Protection Bureau Director Richard Cordray, who pressed ahead with his agenda in defiance of Republicans.

The move is one of the final steps in killing a CFPB rule barring fine-print requirements for arbitration in contracts between consumers and banks. The House voted 231-190 in July to overturn the rule. The resolution now goes to Mr. Trump, who is expected to sign it into law. The White House released a statement late Tuesday praising the Senate action and referring to a recent Treasury Department report that criticized the rule.

The vice president has broken Senate ties five times so far in the Trump administration.

Republican senators Lindsey Graham of South Carolina and John Kennedy of Louisiana sided with Democrats in opposition to the measure.