The gains, however, came on a mixed day for the rest of Asia, while Paris tumbled more than two percent on news that France's newly appointed prime minister had stepped down, compounding a political crisis in the country.
News of the victory for Sanae Takaichi -- who is expected to become prime minister this month -- fanned a fresh wave of optimism on Japanese trading floors as she has previously backed aggressive monetary easing and expanded government spending.
Expectations the Federal Reserve will cut interest rates this month continue to support risk assets, with the S&P 500 and Dow both hitting peaks along with bitcoin and gold.
After her victory Saturday, Takaichi pledged first to implement measures to address inflation and boost Japan's economy, rural areas and primary industries.
Takaichi "looks more inclined than the others to juice the economy", said Taro Kimura at Bloomberg Economics.
"Still, with inflation rising and long-term (bond) yields climbing, she will have to balance her stance with reality, in order not to accelerate cost-of-living squeeze and jolt the rate market," Kimura added.
The Nikkei 225's surge came as the yen weakened more than one percent to top 150 per dollar, while it hit a record low against the euro, touching 176.25 to the single currency.
"An immediate market reaction is likely to be a return of a so-called 'Takaichi trade', which means higher equity prices (except banks), yen depreciation, and higher super-long bond yields," said Masamichi Adachi, UBS Securities chief economist for Japan.
Yields on 30-year Japanese bonds also rose sharply, reflecting fears the country's already colossal debt will balloon further.
Takaichi's win also raised questions about the chances of more Bank of Japan rate hikes, adding to downward pressure on the yen.
There were also gains in Singapore and Mumbai, but Hong Kong, Sydney, Wellington, Manila and Bangkok were all in the red.
Sentiment remains up, though, as bitcoin hit a new peak of $125,689 on Sunday.
Gold pushed past $3,945 and closer to $4,000 Monday, with the US shutdown and expected rate cuts boosting its attractiveness.
The plunge in Paris's CAC 40 index came after France's President Emmanuel Macron accepted Prime Minister Sebastien Lecornu's resignation, plunging the country further into political deadlock.
Macron appointed Lecornu last month but the largely unchanged cabinet lineup he unveiled late Sunday was met with fierce criticism across the political spectrum.
London's FTSE dipped in the morning, after ending last week at a record, while Frankfurt also sank.
US futures were all up.
The closure of parts of the US government dragged into a second week after senators voted for a fourth time to reject a funding fix proposed by Republicans.
Federal agencies have been out of money since Wednesday -- with several public services crippled -- as a result of deadlocked talks.
The row meant key jobs data used by the Fed to guide it on monetary policy was not released when due on Friday.
Still, observers say recent reports indicating the labour market is slowing would likely be enough to cut rates at the next meeting at the end of the month, with other readings on inflation due beforehand.
"It's still likely that the shutdown will end in relatively short order, allowing for the release of the September jobs report before the October (policy) meeting," said economists at Bank of America.
"But even if the first print of September payrolls is solid, doves on the committee will likely point to the recent trend of downward revisions to make the case to keep cutting.
"And given (Fed chief Jerome) Powell's recent dovish pivot, that argument is likely to carry the day."
Oil jumped more than one percent after OPEC+ agreed at the weekend to boost supplies by 137,000 barrels a day -- less than initially expected.
- Key figures at around 0810 GMT -
Tokyo - Nikkei 225: UP 4.8 percent at 47,944.76 (close)
Hong Kong - Hang Seng Index: DOWN 0.7 percent at 26,957.77 (close)
London - FTSE 100: DOWN 0.1 percent at 9,477.95
Shanghai - Composite: Closed for a holiday
Dollar/yen: UP at 150.01 yen from 147.45 yen
Pound/dollar: DOWN at $1.3445 from $1.3482
Euro/pound: DOWN at 86.75 pence from 87.09 pence
Euro/dollar: DOWN at $1.1664 from $1.1742 on Friday
West Texas Intermediate: UP 1.3 percent at $61.66 per barrel
Brent North Sea Crude: UP 1.3 percent at $65.34 per barrel
New York - Dow: UP 0.5 percent at 46,758.28 points (close)
dan/mtp
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