The 5-to-4 ruling almost surely means the 2018 elections will be conducted in the disputed congressional and legislative districts.
The justices gave no reasons in their one-paragraph statement granting a request from Texas that it not be forced to draw new districts until the Supreme Court reviewed the lower court's decision.
But the court's liberals - Justices Ruth Bader Ginsburg, Stephen Breyer, Sonia Sotomayor and Elena Kagan - signaled their unhappiness by noting they would not have agreed to Texas' request.
The court's intervention was a victory for Texas Republicans, who had drawn the districts. It disappointed civil rights groups, who had noted that even though growth in the state's Hispanic population was the reason for additional congressional seats, none were drawn to favor minority candidates.
The decision was yet another indication of the influence of President Donald Trump's nominee to the Supreme Court, Justice Neil Gorsuch, who joined the court in April. Without a full complement of five conservative justices, the court likely would have tied 4 to 4, and Texas's request for a stay would have failed.
The state has been in the midst of an extraordinary losing streak in federal courts over the way it conducts elections.
Over the latter part of the summer, federal judges in four separate cases ruled that the Texas Legislature discriminated against minorities in drawing congressional and legislative districts, setting ID requirements for voters and even regulating who can assist voters for whom English is not their first language.
Two courts are considering whether the actions were intended to discourage African American and Hispanic voters. If the courts find that the efforts were intentional, it could return Texas to the kind of federal oversight from which the Supreme Court freed it and other mostly Southern states in the landmark 2013 decision in Shelby County v. Holder.
Texas Attorney General Ken Paxton (R) called the rulings "outrageous" and "astonishing."
A lower court overseeing the redistricting cases called for a special session of the Texas Legislature to redraw the electoral lines. But Paxton went quickly to the Supreme Court, saying it would be a waste of time if the Supreme Court ultimately agreed with Texas that the districts did not have to be redrawn.
The decision by a three-judge panel ordering new districts "is not just wrong, but egregiously so," Paxton told the court in a brief.
Without a special session or a court redrawing the legislative and congressional district lines, it would seem impossible to have the new districts in place in time for the 2018 elections. New districts would likely have increased the chances for Democrats and minorities to capture them.