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.
Asian shares headed higher on Thursday as rising oil prices boosted energy and mining shares in the region.