Australia's Electoral Commission on Monday said Dr Phelps was leading Mr Morrison's Liberal candidate by almost 1700 votes, with 3000 postal votes yet to be counted.
Phelps received a fillip during the day after a recount found some errors in preference tallies in the Bondi Beach and Bellevue Hill booths.
He paid tribute to Dr Phelps, as well as the Labor candidate Tim Murray, and Mr Turnbull and his wife Lucy.
On a two-candidate basis Phelps is now leading the Liberals Dave Sharma 51.1% to 48.9%.
Scott Morrison, who replaced Mr Turnbull as PM, downplayed his former colleague's decision not to help the party campaign in Wentworth.
"Thank you to the people of Wentworth for placing your trust in me", she said in her victory speech.
Turnbull had, however, resisted direct Australian participation in US-led "freedom of navigation" provocations in Chinese-claimed waters in the South China Sea, and had expressed concern over the bellicose "America First" policies of Donald Trump.
Phelps did not confirm if she would support a new motion against Peter Dutton in relation to possible section 44 violations or a no confidence motion against the government.
"To actually see the Labor Party going backwards I think is reflective of the public's mood towards Bill Shorten", Sydney Liberal MP Trent Zimmerman said on ABC.
"In that time we had been able to legislate, run the Parliament and we haven't lost a single vote".
'Cheaper' Tesla Model 3 nowhere near $35K promised
Expect the model with the standard battery to arrive in the next four to six months, Tesla says. It will be sporty, accelerating from zero to 60mph (0-100kph) in under six seconds.
But by Sunday evening, his candidate trailed an independent rival by 1,600 votes with several thousand votes still to be counted, the Australian Electoral Commission said.
She said on Sunday: "The government and all governments should go full term unless there are exceptional circumstances, and the next election is due in May next year and that's time enough".
Slammed by critics as a cynical bid to garner Jewish votes in the by-election, Morrison's statement was welcomed by Israeli Prime Minister Benjamin Netanyahu, but sparked concern among Palestinian officials and leaders in Indonesia, the world's largest Muslim-majority nation. The prime minister said the result wasn't unexpected and the government was paying the price for its turmoil.
The government's support for coal and inaction on climate change were key drivers of the protest vote in Wentworth, according to an exit poll conducted by research body the Australia Institute.
Phelps gave tacit backing to a signal from Scott Morrison last week that resettlement in New Zealand was an option if the parliament passed legislation preventing asylum seekers from ever settling in Australia.
Before the Wentworth upset, Morrison had indications of support from the Victorian independent Cathy McGowan and the Queensland crossbencher Bob Katter.
This morning, Dr Phelps revealed her campaign cost around $300,000.
Mr Burke signalled Labor would be unlikely to put forward a no-confidence motion in the government, which would need 76 votes to succeed.
The government was "all over the place" on the Middle East, she said. "I don't buy that argument".