Party whip Nola Marino confirmed Mr Turnbull won 48 votes to 35 for Mr Dutton.
Energy bills rose by up to six times the average wage rise previous year according to the Australian Bureau of Statistics.
A report in The Australian suggests Mr Turnbull had lost confidence of nine Liberal cabinet ministers - half of the Liberal contingent.
Dutton said he supported the prime minister.
Energy policy, Pauline Hanson and Tony Abbott are all contributing factors to Turnbull's woes, Professor Jennifer Curtin says.
The Prime Minister forced his rival to show his hand by declaring all leadership positions vacant as soon as the party room meeting started this morning.
After the vote, Dutton resigned as Home Affairs Minister, moving to the backbench.
But the result - narrow by historical standards for a first strike against a prime minister - sets the Turnbull government up for further instability and the possibility of another ballot before the next federal election.
However, those who didn't support it threatened to "cross the floor" - that is, vote against it in Parliament.
Spokane air quality in the 'very unhealthy' range; 'Tuxedo Junction' concert cancelled
Air quality has deteriorated across the province as more than 500 wildfires burn across British Columbia. Wildfire smoke originating in Canada is now clouding the skies over central and northeast Minnesota.
Gmail Brings Confidential Emails to Mobile
If you choose to have a passcode, the recipient will have to enter the same to view the email content. Find your email set to self-destruct in the Sent folder, open it, and tap "Remove Access".
Bill Maher Taunts Trump Over Omarosa: 'He Lost His One Black Friend'
She said this week she chose to release the recordings to prove she is not lying about what happens inside the White House. The discussions about a position with the campaign took place in numerous phone calls over the course of several weeks".
But the move has failed to silence conservative critics within the Coalition.
"I think there might be a second phase strategy here".
He said although most government lawmakers supported the target of reducing Australia's greenhouse gas emissions by 26 per cent below 2005 levels, that support was not enough.
Mr Turnbull's risky move may have backfired as it exposes the weakness of his position and the size of the split between the two factions of the Liberal Party.
"We're for lower prices, Mr Shorten is for higher prices", he said.
"In politics you have to focus on what you can deliver", Mr Turnbull told reporters on Monday.
There was also a vote on the deputy leadership but Foreign Minister Julie Bishop was the only candidate, despite speculation that Health Minister Greg Hunt had his eyes on the post.