The Apple case is seen as a consequential test for Margrethe Vestager, the European commissioner for competition. Ms. Vestager’s role was expanded this month, making her the world’s most powerful regulator. She will continue as antitrust commissioner but will have additional powers as digital and technology regulator in issues like data privacy, cybersecurity and artificial intelligence. Starting Nov. 1, Ms. Vestager will be able to make rules that affect tech firms and initiate cases when she thinks those rules are being broken.

On Tuesday, the European Union court ruled for the first time that the commission has the power to verify whether tax rulings granted by member states to individual companies confer an advantage under national law and therefore are in breach of European competition law. If an advantage is proved, such tax rulings should be considered illegal state aid, the court ruled, incompatible with the rules of the bloc’s internal market.

The court also upheld the commission’s calculation of €30 million in illegal state aid granted to Fiat Chrysler, and cleared the way for Luxembourg to recoup the money immediately.

Fiat did not publicly respond to the ruling on Tuesday. It can appeal to the European Court of Justice, the highest court in the bloc. Luxembourg’s Finance Ministry said it would take time to “analyze the judgment.”

In a similar case involving a deal Starbucks made with the Netherlands, the court again upheld the commission’s jurisdiction over selective tax rulings. But it annulled a €25.7 million fine, saying that the commission did not sufficiently demonstrate any advantage for Starbucks under Dutch law.