Japan's Nikkei rose 0.8 percent to its highest since late April as a softening yen burnished the outlook for the country's exporters. Australian stocks added 0.6 percent and Taiwan 0.3 percent.
Markets elsewhere were more mixed, leaving MSCI's broadest index of Asia-Pacific shares outside Japan flat.
South Korea's main index slipped 0.6 percent after data showed Samsung Electronic's decision to scrap its Galaxy Note 7 dragged on the entire economy in the third quarter, though growth still pipped forecasts.
Wall Street had taken encouragement from upbeat corporate results and the Dow ended Monday up 0.46 percent, while the S&P 500 gained 0.47 percent and the Nasdaq 0.91 percent.
Over one third of U.S. companies have now reported and 80 percent have beaten market expectations. Another third of the S&P 500 components are scheduled to report earnings this week, including heavyweights Apple, Alphabet, Amazon and Boeing.
Merger and acquisition activity added an extra fizz in the wake of AT&T Inc's $85.4 billion bid for Time Warner Inc, though the deal seemed destined to face stringent scrutiny from regulators.
Aiding risk sentiment was the Markit survey of U.S. manufacturing which climbed to a one-year top of 53.2. Business activity in the euro zone also expanded at the fastest pace this year so far in October and firms raised prices at the sharpest rate in more than five years.
The better news led investors to nudge up the probability of a December rate hike from the Federal Reserve to around 74 percent and pressured Treasury prices.
It also lifted the U.S. dollar to a nine-month high against a basket of major currencies at 98.846. The dollar firmed on the yen to 104.43, threatening the month's peak at 104.62, while the euro struggled at $1.0870.
One mover was the Canadian dollar which rebounded from a seven-month low after Bank of Canada Governor Stephen Poloz said the decision on whether to cut interest rates again was not one to take lightly.
The comments countered recent speculation about an imminent easing and nudged the U.S. dollar down to C$1.3345 from a peak at C$1.3398.
In commodities, oil prices dipped on news of the impending restart of Britain's Buzzard oilfield and Iraq's wish to be exempted from OPEC production cuts.
Brent was down 6 cents at $51.40 a barrel, while U.S. crude also lost 6 cents to $50.46.
(Reporting by Wayne Cole; Editing by Eric Meijer and Joseph Radford)
By Wayne Cole