A Christian priest, Rafael Warnock, who is the Democratic Party's candidate, defeated the Republican incumbent Kelly Loeffler by 1 per cent of the votes in the elections held on Tuesday.
Democrat Jon Ossoff had a 0.8 per cent lead over the sitting Republican Senator Davd Perdue as of 1.30 a.m. Georgia time.
But it will likely take some days before the results are finally announced officially as challenges and recounts are almost certain.
Republicans have 50 seats in the 100-member Senate while the Democrats with their two Independent allies have 48 seats, and if the two Georgia Democrats are declared winners, the party will control the Senate as Kamala Harris, who will be the vice president, will have the casting vote as the chair.
The Senate gains would soften the Democratic Party's net loss of 13 seats in the House of Representatives in the November election.
Warnock made a victory speech on Wednesday morning declaring that he "was going to the Senate" to serve all of the state's people.
Loeffler did not concede the election and told her supporters that it was "a game of inches" that she would win.
Both the Republicans had led in the November election, but under the chaotic US system of state-mandated election systems, in Georgia there had to be runoff elections as neither of them got more than 50 per cent of the votes because other candidates were in the races.
Unlike in Georgia, most other states declare the candidate who gets the most number of votes the winner without the 50 per cent and runoff requirements.
If the two Democrats are finally declared winners, President-Elect Joe Biden will have full control of the legislature, although it will be moderated by policy challenges to his moderate orientation from his party's left and progressive groups.
President Donald Trump would be blamed for Republican losses because after losing the November election he continued a quixotic quest to have it overturned creating a distraction and simultaneously fighting with Georgia's officials belonging to his party because they would not back him.
In a recording of a phone call obtained by the Washington Post, Trump was heard asking Georgia Secretary of State Brad Raffensperger to find him "11,780 votes" that would nullify Biden's win in the state.
Raffensperger, who is in charge of Georgia's elections and is a Republican, told him he could not do it, according to the recording.
This episode impacted the party's standing.
Warnock, who is a priest of the Christian Baptist sect to which Harris belongs, will be the first African American elected to the Senate from Georgia.
Both parties poured money and people into the Georgia elections as the state, which was once staunchly Republican, was seen changing politically.
According to the Center for Responsive Politics, the Georgia contests "are the top two most expensive congressional elections ever - by a large margin."
It reported that the candidates and outside groups had spent $470 million in the Perdue versus Ossoff race and $363 million in the Loeffler versus Warnock contest as of Monday and the amounts were expected to increase further.
There are only 7.2 million registered voters in the state.