Japan's main stock index ended 2013 at its highest level in more than six years, closing out its best year since 1972, though most other markets were lacklustre ahead of the new year holiday.
The Nikkei 225 gained 0.7% to 16,291.31, its highest close since late 2007.
Prime minister Shinzo Abe, whose government launched a huge stimulus effort to drag the economy out of a two-decade period of stagnation, took time out from his holiday to celebrate the trading close.
"Thanks to our efforts, the economy went from minus to positive," Mr Abe said. With winter bonuses up, he said: "You have to use that money, keep it moving."
Elsewhere, markets were more cautious. Germany's DAX index drifted 0.4% lower to 9,552.16, while France's CAC shed 0.1% to 4,273.98. Britain's FTSE 100 fell 0.4% to 6,726.84.
In the US, the Dow was up 0.1% at 16,484.87, while the S&P 500 was down the same rate at 1,840.57
This was a banner year for many markets, with the DAX up 25.5%, the CAC index up 17.5% and the FTSE 100 gaining 14%. But none matched the Nikkei 225, which soared 56.7% in 2013 on renewed confidence in the economy after years of feeble growth.
Easy liquidity from government spending and monetary policies aimed at fuelling inflation boosted shares, though the potential for continued strong gains remains uncertain.
For now, Mr Abe can point to the share rally as evidence his "Abenomics" policies are yielding results.
"The Nikkei still looks to round off what has been an astonishing year ... its best year since 1972," Chris Weston of IG Markets said in a commentary, noting that the gain in that year was 92% and unlikely to ever be beaten.
"For those looking for volatility, the Nikkei will remain a major focus for traders in 2014," he said.
Japanese shares will get support in coming months from newly established individual savings accounts, called NISA, that are expected to draw a significant share of household savings into the market.
For the rest of Asia, 2013 has turned out to be much less exuberant.
Hong Kong's Hang Seng Index, burdened by rising concern over debt and slowing growth in mainland China, has gained just 2.4% this year. On Monday, it edged 0.2% lower to 23,209.25.
The Shanghai Composite Index fell 7% this year and extended that loss on Monday, drifting 0.1% lower to 2,098.77.
Still, a correction in the Hong Kong and China markets earlier in the month has put shares at a stable level, said Kwong Man Bun, an analyst at KGI Securities in Hong Kong.
"The market is still quite cautious, but confidence is still there," he said. "There is a holiday mood, but turnover has not yet recovered."
Elsewhere in Asia, shares rose in Australia, South Korea, Singapore, Indonesia, Malaysia, Taiwan, mainland China and New Zealand. India share prices fell, while markets in Thailand and the Philippines were closed for holidays.
In foreign exchange markets, the dollar was trading 0.1% lower at 105.13 Japanese yen, while the euro rose 0.3% to 1.3797 dollars.
Oil prices remained above 100 dollars, with benchmark US oil for February delivery down 24 cents to 100.08 dollars in electronic trading on the New York Mercantile Exchange.