The leader of the Scottish Conservatives was welcomed onto the stage in Manchester with a standing ovation for spearheading the party's advance in Scotland.
Davidson spoke of the need for unity after a weekend of party in-fighting, with foreign secretary Boris Johnson undermining May by publishing his four Brexit "red lines" in the media.
"In government and across the United Kingdom, we must be united behind our Prime Minister," she said.
She highlighted the need for government policy to take into account the views of everyone in the UK, regardless of how they voted in both the Scottish and the EU referendum.
"We're not Leavers or Remainers anymore, we're just Brits," she said.
Davidson also used her speech to attack Labour leader Jeremy Corbyn, saying that the success of the Tory party in Scotland demonstrated how quickly the balance of politics can change.
"Folks, he hasn't even won a raffle yet," she said.
Referring to how her party has stifled the rise of the Scottish National Party, Davidson added: "So too can the Corbyn bubble be burst, but only if we work hard to make it so."