The Senate approved the plan 18-12.
The House adopted a different map last week. The two chambers are expected to try to work out a compromise between the two maps in a conference committee.
The Senate vote marks the first time this year redistricting has been debated on the Senate floor, after several months of political warfare that included Democratic walkouts in the Senate and House and two fruitless special sessions.
Republicans say the map could give the GOP an additional three to five seats in the state's congressional delegation, which is now ruled 17-15 by Democrats.
Democrats fought the plan during often tedious debate over two days. They gave lengthy speeches, peppered the map's author with questions and tried parliamentary maneuvers to postpone a vote.
Republicans, who rule the Texas House and Senate and occupy each statewide-elected office, say the state should have more Republicans representing it in Washington.
Democrats have been fighting Republican redistricting efforts since this spring.
House Democrats fled to Oklahoma during the regular legislative session in May to block a quorum on the issue.
During a second special session, 11 Senate Democrats bolted to Albuquerque, N.M., for 45 days to thwart a quorum in their chamber. They returned last week after the end of the special session when one of their own broke ranks, saying he believed they should take their fight to the Senate floor.
Republican Gov. Rick Perry has said that if lawmakers did not get a redistricting map approved during this session, a fourth session would be needed.