The Senate, breaking ranks with the House, voted yesterday to permit tax-paid lawyers for the poor to engage in courtroom battles for school desegregation.

Debating for the third straight day a bill to extend the life of the Legal Service Corp., the senators voted 35 to 38 to repeal a ban on legal services lawyers participating in such cases.

The prohibition was enacted in 1974, when the corporation was created to take over legal assistance to the poor.

The Office of Equal Opportunity had offered the legal help from 1966 to 1974.

Sen. Dewey F. Barlett (R. Okla.) urged the Senate to retain the ban, arguing that desegregation cases often result in large-scale court-ordered busing, which is opposed by many people.

Bartlett said texpapers should not be required to subsidize such lawsuits.

Sen. Gaylord Nelson (D. Wis.), floor manager for the legal services extension bill, supported Bartlett's amendment to retain the ban even though he opposed it in the Senate Human Resources Committee.

Nelson said an earlier House vote to keep the ban means the prohibition will probably be retained when the two chamgbers reconcile their different bills in a conference committee.

He also noted that legal services lawyers rarely handled desegregation cases prior to the ban. He said they took part in only about 50 such cases, compared with about 7 million cases they have handled since 1966.

Opponents of Bartlett's amendment said it would be unfair to the poor.

"The hands of the Legal Servics Corp. should be freed, and that's all we're doing," said Sen. Jacob K. Javits (R.N.Y.), "The poor man should have the same rights as the one better able to take the case into court."

Earlier, by a vote of 67 to 23, the Senate, rejected an amendment by Sen. Jesse A. Helms (R.N.C.) to have the legal sevices program administered by the states.

Legal services lawyers represented poor people in welfare, housing and other areas.