A divided Supreme Court Tuesday let stand a lower court’s decision that allows unions to collect dues even from nonmembers to assist in collective bargaining, in a case that highlights the absence of the late Justice Antonin Scalia.

Given his questioning during oral arguments last year, it’s likely Scalia would have sided with teachers challenging the union rules, expanding individual workers’ rights at the expense of labor unions. Without Scalia, the court split 4-4, meaning the federal appeals court’s ruling against the teachers will remain in effect.

Analysts expect other ties as the justices begin to reach the end of this term and grapple with the most divisive cases, which now are likely to end in 4-4 rulings, split ideologically between the court’s four members appointed by Democratic presidents and the four Republican-appointed justices.

“If you have any hot-button issue — immigration, I think, will be another — I think you can expect a 4-4 vote,” said Richard Epstein, a professor at the New York University School of Law. “You’re likely to get more of these 4-4 votes, and it’s likely they occur in bigger cases.”

The immigration case involves President Obama’s claims of executive power to grant a temporary deportation amnesty to illegal immigrants. Other cases include voting rights and challenges to the contraceptive mandate under Obamacare.

Mr. Epstein said the court has been through periods like this before. In the years immediately following World War II, Justice Robert H. Jackson was absent while leading the prosecution of Nazi war crimes at Nuremberg, leaving the court evenly split on cases.

But Mr. Epstein said the court is now more ideologically polarized and faces more intensive scrutiny, heightening the interest in Tuesday’s ruling and the expected tie votes.

The ruling Tuesday stemmed from a challenge lodged by California teachers who objected to paying dues to a labor union, saying they disagreed with the union’s spending to lobby government for smaller classes and more generous teacher benefits.

Under a 1970s Supreme Court ruling, nonunion workers can opt out of paying dues that go toward political operations, but states can require them to pay dues that fund other operations, such as collective bargaining.

Public-sector labor unions, however, have blurred the line, given that their collective bargaining positions inherently involve public policy issues. In California, that amounts to $600 or $700, according to the Center for Individual Rights, which pursued the case on behalf of 10 teachers.

During oral arguments, the court’s conservative justices seemed to be pushing for a new standard that would free public-sector workers from the obligation to pay dues, while the liberal justices suggested that would give workers benefits they hadn’t paid for.

Tuesday’s brief ruling didn’t get into any of those issues and instead merely said a lower appeals court’s decision stands.

“The judgment is affirmed by an equally divided court,” the high court said.

The Center for Individual Rights said it will seek a rehearing of the case, known as Friedrichs v. California Teachers Association, hoping the tie ruling can be broken.

“With the death of Justice Scalia, this outcome was not unexpected,” said Terry Pell, president of the center. “We believe this case is too significant to let a split decision stand, and we will file a petition for rehearing with the Supreme Court.”

Labor unions cheered the ruling and rejected the idea of a rehearing.

“Unions are about giving workers and their families a voice on the job and a fair shot to get ahead, and today’s decision enables those aspirations,” said Randi Weingarten, president of the American Federation of Teachers.

The 4-4 ruling reverberated on Capitol Hill, where the battle to replace Scalia is underway.

Mr. Obama has chosen appeals court Judge Merrick Garland to fill the seat, but Republicans who control the Senate, which makes final decisions on nominations, have said Mr. Obama is a lame duck and the pick should be left to his successor.

Democrats, even as they cheered a 4-4 ruling that wouldn’t have been possible with Scalia still alive, said the decision shows why Judge Garland needs to be confirmed.

Republicans, meanwhile, lamented the decision and said Judge Garland would have guaranteed only a 5-4 victory for the labor unions.

With Judge Garland nominated only two weeks ago, he would not have been able to be part of Tuesday’s ruling. It’s also unlikely, even with a hypothetical Republican-controlled Senate eager to approve him, that he would be seated in time to weigh in on the contraceptive, voting rights and immigration cases still pending.

But even a full nine-justice court doesn’t end the chance for tie rulings, because justices can recuse themselves from cases. Justice Elena Kagan did not sit for the hearing of a landmark affirmative action case this term, presumably because she worked on the case as part of the Obama administration.

That left just eight justices to decide. But that case, dubbed Fisher II because it’s the second time it has reached the high court, was likely to be a 5-3 split with Scalia, and now analysts predict it will be a 4-3 split.