Japan's Nikkei index closed at its highest level for two weeks, with exporters boosted by a weaker yen and airlines helped by falling oil prices.
The Nikkei 225 closed up 211.35 points, or 1.2%, at 17,459.85.
Shares in exporters rose as the dollar went above 118 yen. A weaker yen helps make Japanese exports more competitive.
Falling oil prices and the prospect of cheaper fuel pushed Japan Airlines' shares up 5.3%, while rival All Nippon Airways jumped 7.4%.
The decision by oil producers' group Opec on Thursday to maintain current output levels sent the price of oil down sharply. Brent crude was trading at $72.49 a barrel on Friday having fallen by more than $5 on Thursday.
Investors were also digesting a large amount of economic data from Japan, which painted a mixed picture of the world's third-largest economy.
Excluding the effect of a large tax rise in April, the inflation rate in October was 0.9%, way below the 2% target.
Including the tax rise, core inflation was 2.9% higher in October than a year ago, compared with 3% in September.
Household spending fell by 4% in the year to October, but retail sales rose 1.4%, beating expectations and the unemployment rate fell from 3.6% to 3.5%.
Japan's industrial output rose by more than expected, climbing 0.2% in October from the previous month - the second consecutive month of gains.
In Australia, the benchmark S&P/ASX 200 index closed down 1.6% at 5,313, its biggest percentage drop in seven weeks.
Shares in the resources sector were weighed down by the slump in oil prices following the Opec meeting.
In South Korea, the Kospi index closed down 0.1% at 1,980.78.
Source - BBC News