The parliament, which will have the final say on any Brexit deal, became the first EU body to take a formal stand on the talks, just a week after British Prime Minister Theresa May formally triggered the process for leaving the bloc.
The vote was 516 for, 133 against and 50 abstentions.
"You will set the tone for Britain," the bloc's Brexit negotiator Michel Barnier told MEPs in Strasbourg, France, just before the vote.
He said the message on phased negotiations should be that "the sooner we agree the principles of an orderly withdrawal, the sooner we can prepare our future relations in trade."
The EU has rejected May's call in her letter for talks on the terms of the divorce and on a future trade deal to be held in parallel.
The resolution won the backing of all the major groups in the parliament, from the conservative European People's Party (EPP), the biggest bloc, to the Socialists and Democrats alliance, as well as the ALDE liberals, the Greens and the leftist parliamentary group GUE.
"It's key to have a united European parliament together with the EU negotiator and the European Council," Guy Verhofstadt, the Liberal leader and parliament's Brexit negotiator, told MEPs.
The EPP's German leader Manfred Weber told the assembly "we want a fair and constructive atmosphere," but warned Britain cannot get a better deal leaving than staying inside the bloc.
He also said the EU will insist Britain pay for its outstanding financial commitments until it leaves the bloc and will seek assurances over the border between EU member Ireland and Northern Ireland, which is part of the United Kingdom.
"Irish interests are not just Irish interests, they are also European interests," Weber said.
The guidelines, which Weber calls 'red lines', reinforce the draft guidelines unveiled last Friday by EU President Donald Tusk, who represents the member states.
But the 27 countries will not formally approve the Tusk guidelines until a summit on April 29.
"People cannot end up being simply a negotiating chip," said European Commission chief Jean-Claude Juncker.
Immigration helped fuel the Brexit campaign which culminated in the shock vote by Britons last June to leave the bloc.
Tusk's guidelines call for "sufficient progress" on divorce terms before a new trade deal is struck, as well as protections of the rights of EU citizens and the border in Northern Ireland.
The Brexit talks have already got off to a difficult start after London was alarmed by a clause in the guidelines saying Spain had to be consulted on any post-Brexit trade deal that affects the British outcrop of Gibraltar.
Brexit champion Nigel Farage blasted the EU over its demands to negotiate divorce terms before striking a post-Brexit trade deal, as well as its stance on Gibraltar and its multi-billion dollar exit bill.
Farage compared the EU to the "mafia" that is holding Britain hostage for a ransom, sparking jeers from many MEPs and a rebuke from the parliament's Italian chief Antonio Tajani, who called his remarks "unacceptable."
Farage fired back: "Mr President, I do understand national sensitivities. I will change it to gangsters and that is how we are being treated. We are being given a ransom note."
Verhofstadt said he regretted the British vote to leave the EU, but suggested a future young generation might return to the European fold.
The parliament is likely to hold a vote on any final Brexit deal at the end of 2018 or in early 2019.
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