The Hungarian foreign minister, Péter Szijjártó, called the vote "petty revenge" against his country's tough anti-migration policies.
"Viktor Orban's government has been leading the charge against European values by silencing independent media, replacing critical judges, and putting academia on a leash", Ms Sargentini said.
"Success! The European Parliament has set an extremely important precedent after voting in favour of Article 7 that puts in motion infringement procedures against Hungary for failing to respect fundamental EU values".
"It is a positive sign of this parliament taking responsibility and wanting action", Sargentini told a press conference afterward.
The Sargentini report details a long list of "concerns" regarding violations of European Union freedoms and values in the press, universities, minorities, migrants, and corruption and the independence of the judiciary.
Polish EU parliament members allied with the PiS voted against the measure to censure Budapest, while others with links to centrist parties endorsed it.
"Poland is very anxious by the decision taken by Parliament today", Joanna Kopcinska, spokeswoman for Poland's right-wing Law and Justice (PiS) government told AFP via email.
In a brief speech to parliament on Tuesday, Orban vowed that Hungary would resist any attempt to "blackmail" it into softening its anti-migrant stance, which he charged was the motive behind the vote.
With Britain scheduled to leave the bloc altogether in March and Europeans voting in European Parliament elections in May, the rows over Hungary and Poland highlight tensions between nationalist and federalist camps.
Orban said in a video posted on Facebook that European Union parliamentarians who support migration "are preparing for revenge against Hungary, because Hungarians have decided they will not become an immigrant country".
The group may now consider whether to suspend Orban's Fidesz party.
Even Orban's fellow migration hardliner, Austria's Chancellor Sebastian Kurz, unexpectedly said his party's five European lawmakers would vote against Budapest.
The Commission, headed by EPP member Jean-Claude Juncker, has repeatedly clashed with Orban's government, especially since Budapest refused to admit asylum seekers under an European Union scheme launched at the height of the migration crisis in 2015.
But Guy Verhofstadt, the former Belgian prime minister who leads the liberal democrat party in the European parliament, quoted the late John McCain "who called you a neo-fascist in bed with Putin".
He challenged the legality of the vote saying that not counting abstentions as votes cast is irregular, and they will challenge the vote with the EP's leadership.
However, the vote also revealed sharp rifts, as 197 MEPs voted against the motion and an additional 48 abstained.
"I am in complete agreement with the result", Juncker said.
The German MEP now serves as the head of the center-right EPP in the European Parliament.
Orban has blamed Merkel for Europe's migration crisis, while the Hungarian leader was criticised for breaching worldwide standards and rules on migration and treating asylum seekers harshly.
The vote was hailed as "historic" by Amnesty International's human rights expert Berber Biala-Hettinga.
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