WASHINGTON—Senate Republicans rejected Democrats’ demands to call new witnesses and documents in President Trump’s impeachment trial, clearing the way for an acquittal on abuse of power and obstruction-of-Congress charges next week.

The 51-49 vote late Friday afternoon represented a major victory for Republican leadership, which has sought to complete the trial as quickly as possible and avoid testimony that could be politically damaging. Democrats had spent weeks calling for the Senate to subpoena former national security adviser John Bolton and other officials, seeking testimony about Mr. Trump’s efforts to press Ukraine to launch investigations that could benefit him politically.

Two Republicans, Sens. Mitt Romney of Utah and Susan Collins of Maine, joined every Democrat to vote for the Senate to call in new witnesses. The GOP controls 53 of the Senate’s 100 seats.

Under a separate resolution that Republicans approved along party lines, the impeachment trial will break for the weekend and resume Monday at 11 a.m. EST for four hours of closing arguments. After those arguments, the trial will adjourn again, giving senators the opportunity to speak on the floor about the charges before returning for a vote on the articles of impeachment at 4 p.m. on Wednesday.

Democrats shortly after the vote on witnesses suggested that any acquittal of Mr. Trump would be tainted.