The benchmark Nikkei index at the Tokyo Stock Exchange gained 95.50 points to 9,945.24.
Japanese markets were closed on Friday and will be shut again from Tuesday to Thursday this week for the Golden Week holiday.
"If we think about which risk is bigger as we head into a long holiday, it seems it's riskier to sell now than to buy," said Kenichi Hirano, an operating officer at Tachibana Securities.
Strong US stocks also offset uncertainty on Japanese corporate earnings due to effects related to the March 11 earthquake and tsunami, he told Dow Jones Newswires.
Shares in Sony, which held an unusual Sunday news conference on a security breach, rose 1.99 percent to 2,305 yen.
Sony executives bowed in apology and said the company would begin restoring its shut-down PlayStation Network and Qriocity online services in the next week as it moved to improve security after the breach hit 77 million accounts.
In New York on Friday, US stocks rose modestly, with Dow blue chips spurred by Caterpillar's earnings while the Nasdaq struggled after lacklustre Microsoft results and a poor Research in Motion forecast.
Despite mixed economic data and a tumble in Microsoft shares, the New York Stock Exchange notched up its strongest monthly gain of the year.
The Dow Jones Industrial Average rose 47.23 points (0.37 percent) to finish at 12,810.54 while the tech-rich Nasdaq Composite edged up 1.01 points (0.04 percent) to 2,873.54.