Brent crude futures were up $2.43, or 2.6%, to $95.95 a barrel by 12:31 p.m. EDT (1631 GMT).
U.S. West Texas Intermediate (WTI) crude rose $2.86, or 3.3%, to $88.18.
U.S. crude stocks rose 2.6 million barrels last week, according to weekly government data, more than anticipated, but that was lower than industry figures, which showed a 4.5 million-barrel build.
In addition, crude exports rose to 5.1 million barrels a day, the most ever, dropping U.S. crude imports on net to their lowest in history.
Traders attributed the surge in exports to the widened WTI-Brent spread , which, coming into Wednesday's trade, was at more than $8 per barrel.