In Asian trade, U.S. crude oil futures tacked on 1.09 percent to $48.24 a barrel by 3:43 p.m. SIN/HK time, after rising 3.16 percent by the U.S. settlement, while Brent added 0.63 percent to $49.28 a barrel after settling up 2.38 percent, with both reaching their highest settlement Monday since late last year. The gains came on growing Nigerian oil output disruptions and after long-time bear Goldman Sachs said the market had flipped to a deficit, ending almost two years of oversupply.
"The increasing intensity in supply-side disruptions in the oil market should see prices well supported in the short term," ANZ said in a morning note Tuesday, adding that the rise in crude prices helped to boost commodities and commodity currencies overnight.
In Australia, mining shares gained amid higher commodity prices. BHP Billiton added 3.50 percent, while Rio Tinto was up 1.46 percent.
Apple's suppliers were mixed. Apple closed the U.S. session up 3.7 percent, its best day since March 1, after storied investor Warren Buffett's Berkshire Hathaway said it invested more than $1 billion for a new stake in the company.
In Japan, Apple supplier Japan Display added 2.54 percent and in South Korea, Samsung Electronics, which is both an Apple supplier and competitor, rose 1.28 percent. In Taiwan, Apple-related shares were mixed, with Pegatron down 0.64 percent and Foxconn Technology up 3.43 percent.
Weighing on Australia's benchmark index, shares of National Australia Bank dropped 3.07 percent as the stock went ex-dividend. NAB paid a dividend of 99 Australian cents.
Minutes from the Reserve Bank of Australia meeting showed the committee discussed leaving rates on hold, but ultimately decided that a 25 basis-point interest rate cut to a new record low of 1.75 percent would allow the central bank to better aim at boosting lower-than-expected inflation. The minutes didn't provide much guidance on whether another rate cut might be on the cards.
The news pushed up the Australian dollar, which climbed as high as $0.7366 after the minutes' release, compared with around $0.7280 before the release of the minutes.
China bank shares were mixed, with Bank of China's Hong Kong-listed shares were up 1.34 percent at 3:45 p.m. SIN/HK time, while its mainland-listed ones ended flat.
On Monday, Reuters reported that China's central bank is investigating the accuracy of non-performing loans (NPLs) data at banks, specifically whether NPLs are being mis-categorized, according to two sources who saw a central bank notice on the issue.
Shares of Singapore Airlines shed 1.11 percent by 3:46 p.m. SIN/HK time, leaving the stock down more than 8 percent since the company reported earnings last week that missed analysts' expectations. While lower oil prices helped, yields declined more than expected.
In a note last week, CIMB said the carrier may not deliver earnings-per-share (EPS) growth this year and the bank cut its fiscal 2017-18 EPS forecasts by 29-34 percent, downgrading the stock to "hold" from "add."
Singapore's non-oil domestic exports (NODX) fell 7.9 percent on-year in April, a slower pace than March's 15.7 percent drop and in line with Reuters forecasts. But the figure was supported by a turnaround in the volatile pharmaceuticals sector, with data from Reuters showing April exports in that segment rising 17.9 percent, reversing from March's 30.9 percent drop.
DBS noted that the decline was broad-based, across both electronics and non-electronics products, with exports to all key markets except Hong Kong and Europe falling, highlighting global demand weakness.
"Manufacturers/exporters are still struggling with weak demand and this will eventually manifest itself in the headline gross domestic product growth figures. All is not well on the external front," DBS said in a note Tuesday after the data.
The Dow Jones industrial average closed up 175.39 points, or 1 percent, at 17,710.71, the S&P 500 closed up 19.92 points, or 0.97 percent, at 2,066.53 and the Nasdaq composite closed up 57.78 points, or 1.22 percent, at 4,775.46.
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—By CNBC.Com's Leslie Shaffer; Follow her on Twitter @LeslieShaffer1