Investors shrugged off data that showed core consumer prices fell 0.1% in August from a year ago - the first annual drop since April 2013.
The decline in prices, which includes oil products but not fresh food, had been expected by economists.
Japan's benchmark Nikkei index ended up 1.8% at 17,880.51.
Shares in Sharp fell as much as 10% after the Nikkei business daily said it was likely to report a half-year loss of 30bn yen ($250m; Â£163m) as a result of weak sales of LCD panels for smartphones.
On the currency markets, the US dollar rose in Asian trade after the head of US Federal Reserve Janet Yellen said the central bank was still on track to raise interest rates later this year.
The dollar was up to 120.32 yen from around 120.00 yen before her speech.
In China, investors continued to digest the mixed news coming out of the economy this week.
A preliminary reading of China's factory activity fell to the weakest level since 2009, but home prices rose for the fourth month, indicating growth.
The Shanghai Composite closed down 1.6% at 3,092.35, while Hong Kong's Hang Seng index rose 0.4%  to 21,186.32.
In Australia, the S&P/ASX 200 index closed down 0.6% at 5,042.10.
South Korean shares fell despite a central bank survey showing consumer sentiment had hit a four-month high in September.
The benchmark Kospi finished down 0.2% at 1,942.85.
Japanese shares finished higher on Friday, recovering some of the losses in the previous session when the market lost nearly 3%.