The House of Commons turned down the Conservative proposal by 311 votes to 248 - a margin of 63.
The result means Parliament itself will decide whether to ratify the treaty, signed by EU leaders last December.
Thirteen Lib Dem MPs rebelled against the party's orders to abstain on the referendum vote, with three frontbench spokesmen resigning their posts.
MPs rejected the Conservative amendment to the EU (Amendment) Bill, but 29 Labour MPs supported it. Three Tories defied their party leadership.

Manifestos
All EU parliaments must ratify the treaty before it can come into force. The only country which has committed to a referendum is Ireland.
The three main UK political parties promised a public vote on the EU Constitution in their 2005 general election manifestos.
But the constitution was rejected by the French and Dutch electorates later that year. The Lisbon Treaty was drawn up to replace it.
The government and the Lib Dems say the treaty does not have constitutional implications, so a referendum on it is not needed
The government says most changes are minor and procedural and it has secured "opt-outs" where necessary.

Month-long debate
But the Conservatives, some Labour and Lib Dem MPs and the UK Independence Party among others, say that it is effectively the constitution under a different name - so there should be a referendum.
Shadow foreign secretary William Hague said: "This treaty will now go to the House of Lords.
"It is convention that the House of Lords does not stand in the way of manifesto commitments. We hope that in this case the Lords will hold the government to their manifesto commitment.
"The Liberal Democrats' position will once again be pivotal. We will see if they follow their three-line whip in the Commons to abstain."
The Lib Dem leadership, which instead wants a referendum on whether the UK should stay within the EU, ordered its MPs to abstain in the Tory-led debate.
But 13 refused to do so, instead voting for a referendum on the treaty.
Scottish affairs spokesman Alistair Carmichael, countryside spokesman Tim Farron and justice spokesman David Heath resigned from the Lib Dem frontbench team.