The gains came despite a tepid lead from Wall Street, where healthy housing figures were offset by disappointing eurozone economic data.
Tokyo rebounded from early profit-taking to end a touch higher, adding 6.96 points to 15,376.24 — a five-month high — while Seoul jumped 0.98%, or 19.43 points, to 1,994.35.
Hong Kong rebounded slightly after Monday's heavy selling, rose 0.33%, or 75.83 points, to 22,880.64, while Shanghai advanced 0.47%, or 9.56 points, to 2,033.93,
However, Sydney fell 0.38%, or 20.5 points, to close at 5,432.8.
Trade remained uninspired despite a survey on Monday indicating Chinese manufacturing in June growing for the first time this year, raising hopes for the economy.
China's impressive figures were not repeated in the eurozone, where Markit Economics' composite purchasing managers index slipped to its weakest level since December, suggesting a recovery in the bloc could be stalling.
The data showed that growth was still strong in Germany, despite weakening slightly, but that the downturn in France, which is increasingly generating the most worry, is deepening.
In New York, the Dow and S&P 500 edged down marginally after ending last week at record highs, while the Nasdaq was a touch stronger.
The soft close came despite figures showing existing-home sales, which make up most of the housing market, rose 4.9% in May from April, a second straight advance.
On currency markets in Asia the dollar held up, buying 101.92 yen in afternoon trade, compared with 101.94 yen in New York late on Monday
The euro bought $1.3614 and 138.76 yen against $1.3601 and 138.65 yen.
In Japan, Japanese Prime Minister Shinzo Abe is expected on Tuesday to unveil a fresh round of reforms to boost a nascent growth recovery, his second attempt at launching the "third arrow" of his economic action plan.
Among the proposals expected to be put forward is a promise to slash Japan's corporate tax rate — one of the world's highest — and tackle other sectors long protected by government help, reports have said.
Oil prices dipped as investors noted that turmoil in Iraq has yet to directly disrupt production. But they were keeping watch on the country after US Secretary of State John Kerry made a surprise visit there.
US benchmark West Texas Intermediate fell 54 cents to $105.63 and Brent crude eased 63 cents to $113.69.
Gold fetched $1,323.70 an ounce at 1050 GMT in Asia compared with $1,310.60 late on Monday.
In other markets, Taipei rose 0.19%, or 17.85 points, to 9,246.20. PC maker Acer added 1.89% to T$21.6 while smartphone maker HTC was 1.5% higher at T$135.
Wellington fell 0.10% or 4.96 points to 5,122.21. Outdoor apparel firm Kathmandu dived 11.52% to NZ$3.15 after a profit warning and Telecom was off 0.19% at NZ$2.66.
Manila closed 0.46% higher, adding 31.08 points to 6,793.07.
SM Investments gained 2.38% to 818 pesos while Metropolitan Bank and Trust rose 0.29% to 86.95 pesos.
Singapore rose 0.14%, or 4.63 points, to 3,262.03. Agribusiness company Wilmar International gained 0.31% to S$3.21 while oil rig maker Keppel Corp added 0.38% to S$10.72.
Jakarta ended up 0.42%, or 20.11 points, at 4,862.24. Telecoms firm Indosat gained 2.11% to 3,880 rupiah, while coal miner Adaro Energy slipped 1.73% to 1,135 rupiah.
Kuala Lumpur gained 0.44%, or 8.37 points, to 1,892.33. Telekom Malaysia added 0.5% to 6.32 ringgit, while Budget carrier AirAsia fell 0.5% to 2.23 ringgit.
Bangkok lost 0.53%, or 7.78 points, to 1,760.92. Coal producer Banpu closed unchanged at 28.50 baht while Bangkok Bank fell 1.04% to 191.
Mumbai surged 1.35%, or 337.58 points, to 25,368.90. Jubilant FoodWorks gained 7.34% to 1,308.40 rupees while Gujarat State Petronet rose 7.18% to 82.05 rupees.