Tokyo and Sydney advanced while Shanghai and Hong Kong declined.
Seoul swung between gains and losses.
Markets are betting on control of the US Congress being split between Republicans and Democrats, which could mean low taxes and light regulation that investors like stay in place.
On Wall Street, the benchmark S&P 500 index closed 1.9 per cent higher. It is moving toward its biggest weekly gain since April.
I find it remarkable how relaxed these markets are under the circumstances, said Craig Erlam of Oanda in a report.
Hopefully, the faith investors have shown is rewarded, because the last thing we need is an extremely messy conclusion to what has already been a hostile and divisive election.
The Shanghai Composite Index lost 0.5 per cent to 3,302.02 while the Nikkei 225 in Tokyo gained 1.1 per cent to 24,367.35. The Hang Seng in Hong Kong shed 0.3 per cent to 25,617.47.
The Kospi in Seoul was down less than 0.1 per cent at mid-morning at 2,415.67. The S&P-ASX 200 in Sydney advanced 0.9 pere cent to 6,193.20.
New Zealand and Jakarta gained while Singapore declined.
On Wall Street, the S&P 500 rose to 3,510.45. The Dow Jones Industrial Average gained 1.9 per cent to 28,390.18.
The Nasdaq composite climbed 2.6 per cent to 11,890.93.
In the US presidential election, challenger Joe Biden leads in the vote counting, but President Donald Trump and his supporters are questioning the legitimacy of the totals with key states still counting ballots.
Markets are still betting on a clear election outcome (presumably Biden), said Mizuho Bank in a report.
Analysts warn that an extended court battle with no clear winner could increase uncertainty, which markets dislike, and drag down stocks.
Also Thursday, the US Federal Reserve said its key interest rate will be left at a record low near zero.
It reaffirmed its readiness to do more to support the economy under threat from a worsening coronavirus pandemic.
Technology stocks helped power the rally. Rising expectations that Republicans can hold onto the Senate are easing investors' worries that a Democratic-controlled Washington would beef up anti-monopoly laws and go after Big Tech more aggressively.
Apple climbed 3.5 per cent, Microsoft rose 3.2 per cent, and Amazon added 2.5 per cent. Facebook gained 2.5 per cent and Google's parent company rose 1 per cent.
They're also the five biggest stocks in the S&P 500 by market value.
About 82 percent of stocks in the S&P 500 closed higher.
Qualcomm jumped 12.7 per cent for one of the biggest gains after it reported stronger revenue and profit for the latest quarter than analysts expected.
In energy markets, benchmark US crude lost 71 cents to USD 38.08 per barrel in electronic trading on the New York Mercantile Exchange.
The contract fell 36 cents on Thursday to USD 38.79. Brent crude, the international price standard, declined 71 cents to USD 40.22 per barrel in London. It shed 30 cents the previous session to USD 40.93.
The dollar edged up to 103.53 yen from Thursday's 103.51. The euro declined to USD 1.1824 from USD 1.1838.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)