The vote will unlock loans that will help Athens pay its huge debts and ease concerns of contagion through other economies, which many fear could lead to another global financial crisis.
New York's main contract, West Texas Intermediate for delivery in August, climbed 54 cents to $95.31 a barrel after soaring $1.88 on Wednesday.
Brent North Sea crude, also for August, rose 22 cents to $112.62 after leaping $3.62 in New York.
"Yesterday's news of Greece passing its first voting of the austerity bill is very positive as it boosted confidence that it is likely for Greece to pass the final decision tonight," said Serene Lim, a Singapore-based analyst with ANZ Bank.
MPs must vote later Thursday on the detail of the package, which will slash 28.4 billion euros ($40 billion) from government spending by 2015.
The deal had to be passed in order to meet the conditions for 12 billion euros of emergency loans from the European Union and International Monetary Fund that will service Greece's massive debts.
The news cheered investors and sent the euro higher against the greenback, giving a fillip to crude, which is priced in dollars.
Lim said data showing healthy energy demand in the United States, the world's biggest economy, should also bolster oil prices.
The US Department of Energy said on Wednesday that American crude inventories fell 4.4 million barrels last week, exceeding market expectations.
Thinning energy inventories indicate robust demand.
