MPs were asked whether "this House has confidence in Her Majesty's government", with defeat almost certainly triggering a general election.
Mr Jones and Mr Smith voted for the motion, alongside almost all his Conservative colleagues, as it was passed 349-238.
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Selby and Ainsty MP Nigel Adams also voted for the motion.
Voting for the motion were 342 Tory MPs, six DUP MPs and one Independent MP.
Meanwhile, 181 Labour MPs, 37 SNP MPs, 12 Lib Dem MPs, two Independent MPs, one SDLP MP, one Alliance MP, three Plaid Cymru MPs and one Green Party MP voted against it.
There were just 48 who abstained or did not vote – 16 Labour MPs, 12 Tory MPs, seven SNP MPs, two DUP MPs, six Independent MPs, one SDLP MP, two Alba Party MPs and two Lib Dem MPs.
The vote counts do not include the four MPs who acted as tellers, the seven Sinn Féin MPs who do not take their seats, the Speaker or the three Deputy Speakers.