The incoming PM said she was "determined to deliver" for the British people - pledging tax cuts, action on energy bills, and putting the NHS "on a firm footing".
The foreign secretary, who looked visibly startled, said “oh, my god” before leaving the podium.
The culture secretary's behaviour came during a debate on whether MPs have confidence in Boris Johnson's government.
Tugendhat, the MP for Tonbridge and Walling, was eliminated from the Tory leadership contest on Monday night.
There is growing speculation that Boris Johnson could call a snap general election to save his premiership.
The prime minister is facing allegations he attempted to get his wife a top job at the foreign office.
Wednesday proved yet another challenging day for Boris Johnson after shocking details about law-breaking in Downing Street emerged following the publication of Sue Gray's long-gestating report.
Yahoo News UK visits Bury, where voters are united on one thing - they don't much like politicians at the moment.
Imran Hussain was shut down by Speaker Lindsay Hoyle after raising concerns about Islamophobia.
A growing number of experts are suggesting part of the chancellor's energy bill crisis support package is a "loan", rather than a "rebate".
Boris Johnson faced down yet another make-or-break day and seems to have emerged intact - for now. Yahoo News UK's political correspondent, Nadine Batchelor-Hunt, reports on a remarkable 24 hours in Parliament.