Most Conservative MPs voted against delaying Brexit - including seven cabinet members - meaning Mrs May had to rely on Labour and other opposition votes to get it through.
But some Labour frontbenchers resigned to defy party orders to abstain on a vote on holding another referendum.
Shadow housing minister Yvonne Fovargue, shadow education minister Emma Lewell-Buck, shadow business minister Justin Madders, Ruth Smeeth, a shadow ministerial aide, and Labour whip Stephanie Peacock, all quit their roles to oppose one.
Theresa May, who has long insisted that the UK will leave the EU on 29 March with or without a withdrawal deal, voted to delay Brexit.
She had been forced to offer MPs a vote on delaying Brexit after they rejected her withdrawal agreement by a large margin, for a second time, and then voted to reject a no-deal Brexit.
She has warned that extending the departure date beyond three months could harm trust in democracy - and mean that the UK would have to take part in May's European Parliament elections.