Japan's Nikkei 225 rose 2.3% to 69,901.70 on Monday and briefly topped 70,000 for the first time in three months.
Cooling inflation worries drove the move after a softer U.S. jobs report suggested the Federal Reserve is less likely to raise rates again in October.
AI-linked shares led gains in the region, with Tokyo Electron up 5.2%, SoftBank Group adding 3.1% and TSMC rising 3%.
Elsewhere, Sydney's S&P/ASX 200 edged up less than 0.1% and Hong Kong's Hang Seng was flat, while Shanghai and South Korea were shut for holidays.
U.S. stocks ended last week near record highs as the 10-year Treasury yield retreated from a peak near 5.35%, though oil remained volatile with Brent at $101.24.