Mr Sharma, a former Australian ambassador to Israel, is running on 45 per cent of the two-party preferred vote compared to 55 per cent for Dr Phelps, internal Liberal Party polling suggests.
The result of the much-anticipated by-election means the Morrison government no longer holds majority, meaning there is now a hung parliament.
As rain bucketed down on Sydney in what's marked a disastrous night for the Liberal Party, Phelps achieved a swing of more than 20 percent against its candidate Dave Sharma in Malcolm Turnbull's former seat.
The biggest swing in Australia's political history has landed the nation with its second minority government in just over eight years.
He said Saturday's voting booths where skewed to Dr Phelps, showing that there had a been a late surge for her. "So I would encourage people to think about that carefully".
The Saturday poll could make history as the seat in Sydney's east is a renowned "safe" blue-ribbon seat having been held by the Liberals since the party's inception in 1944.
Phelps said she would be setting two priorities - action on climate change and getting asylum seeker children off Nauru.
She might also lend support for a national integrity commission that has been promoted by Labor, the Greens and crossbenchers for some time.
Dr Phelps claimed victory on Saturday night as Liberal candidate Dave Sharma suffered a swing of nearly 20 per cent against him.
At midday AEDT the ABC's election count showed thatDr Phelps had a lead of 884 votes after preferences.
Mr Morrison on Sunday again conceded the electorate had vented its anger at the government for the by-election caused when Malcolm Turnbull quit parliament after being rolled as prime minister.
"Incredible result and proud of the people of Wentworth", Turnbull's son, Alex, tweeted on Saturday night.
The prime minister said the result wasn't unexpected and the government was paying the price for its turmoil. While there is no highly contentious legislation scheduled in the House of Representatives, Morrison will still have to try and manage the hung parliament as he tries to devise a strategy to turn the Coalition's policy platform around.
Phelps, who took the seat made vacant after former PM Malcolm Turnbull's resignation, told the Today show: "The things that I was talking about during the campaign are really important".
"I've certainly said that 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", Dr Phelps told ABC TV.
Independent Bob Katter said he did not want to see the government destabilised or an early election called.