The price of Brent crude oil hit 2015 highs above $63 (??42) a barrel, rallying on government data that showed oil inventories in the US rose less than expected last week.
Tokyo's Nikkei 225 closed up 0.1% at 19,885.77, reversing earlier losses.
Toyota's shares were up 0.4% after the firm said it would end a three-year, self-imposed break from expansion.
The carmaker said it would build a new $1bn plant in Mexico and add a new production line to a plant in China.
Sharp's shares surged 4.5% after sources said it would meet with banks on Thursday for a $1.7bn rescue deal for the loss-making electronics firm.
In Greater China, Hong Kong's Hang Seng index closed up 0.4% at 27,739.71, while the Shanghai Composite was up 2.7% to 4,194.82 - hitting another seven-year high.
Shares on the mainland posted their biggest fall in a month on Wednesday after growth data showed China's economy had slowed further in the three months to March this year.
In Australia, shares were higher on jobs data that came in above expectations.
Employment rose 37,700 in March, more than double the market forecast of 15,000. February's increase was also revised up to show a 41,900 increase.
The spike in hiring drove the unemployment rate down to 6.1%, from January's decade-peak of 6.3%.
The benchmark S&P/ASX 200 index closed up 0.7% to 5,947.5 after ending down for the previous three sessions.
Shares of heavyweight miner BHP Billiton were up 2.4% on the resources sector's gains.
South Korea's benchmark Kospi index finished up 0.9% to 2,139.90 - its highest close since August 2011.
The index has risen for the fifth consecutive day.

The wooden panelling, ceiling beams and fireplace from the Oak Parlour at Gwydir Castle, near Llanrwst, were sold to an American newspaper owner in 1921.
They were shipped to New York but have not been seen since the 1930s.
It is now hoped they can be retraced and brought back to Wales.
Judy Corbett, who owns Gwydir Castle with her husband, Peter Welford, said it was bought by William Randolph Hearst, an American newspaper tycoon in 1921.
The 16th Century linen-fold panelling, the fireplace overmantel and the carved and moulded ceiling beams were dismantled, crated up and sent to America.
"He ended up assembling it in his billiard room in his apartment in New York," she said.
The apartment was known as the Clarendon, said to be the largest apartment in the world.
It was partly demolished in the 1930s, but the couple know the panelled rooms were taken out and stored.
"This is where we lose track of it," they said.
"Where did our room go?
"Did the Hearst family hold on to it?  Was it sold? Was it donated to an American museum?
"We have spent years looking through archives and records but can find no trace of it anywhere."
Numerous items of furniture, along with another whole room, were also sold off in 1921.
The panelling from the dining room was also bought by Mr Hearst.
But it was later discovered in a warehouse belonging to the Metropolitan Museum in New York, and was brought back to Wales and reinstalled at Gwydir in 1996.
Ms Corbett added: "The story of the dining room shows that miracles can happen. We would love to find our second missing room."
Asian shares headed higher on Thursday as rising oil prices boosted energy and mining shares in the region.
[NEXT_CONCEPT]
The owners of a 16th Century Tudor mansion in Conwy county are appealing to people in the United States to help them find a missing room.