* EIA reports surprise drop in U.S. crude inventories
* Net crude imports drop to lowest on record -EIA
* Weaker dollar supports oil prices (New throughout, updates prices, market activity and comments; new byline, changes dateline, previously LONDON)
By Stephanie Kelly
NEW YORK, Feb 22 (Reuters) - Oil prices rallied on Thursday with U.S. crude rising to a two-week high, boosted by data showing a surprise draw in U.S. crude inventories and also by a drop in the dollar.
West Texas Intermediate (WTI) crude futures for April delivery rose $1.05 to $62.73 a barrel, a 1.7 percent gain, by 11:49 a.m. EST (1649 GMT).
Brent crude futures for April delivery rose 78 cents to $66.20 a barrel, a 1.2 percent gain.
U.S. crude inventories unexpectedly fell 1.6 million barrels in the week to Feb. 16, as net imports dropped to a record low and exports surged, according to data from the Energy Information Administration.
Analysts had expected an increase of 1.8 million barrels.
Crude stocks at the Cushing, Oklahoma, delivery hub fell by 2.7 million barrels, the EIA said.
"The reason that the inventories continue to drop at Cushing is because the market remains backwardated and therefore it's uneconomical to be storing crude," said Andrew Lipow, president of Lipow Oil Associates in Houston, Texas.
In a market structure called backwardation, prompt crude prices are higher than forward prices, discouraging storage.
"It makes more sense to liquidate your on-hand inventories," Lipow said.
The EIA said net crude imports fell last week by 1.6 million barrels per day to 4.98 million bpd, the lowest since the EIA started recording the data in 2001.
Exports of U.S. crude jumped to just above 2 million bpd, close to a record 2.1 million hit in October. That helped push net imports to the lowest level on record.
The Louisiana Offshore Oil Port (LOOP), the largest privately owned crude terminal in the United States, completed the first very large crude carrier (VLCC) crude oil loading operation at its deepwater port, the company said on Sunday. The supertankers can ship about 2 million barrels of oil.
Crude inventories typically rise at this time of year, as many refineries cut intake to conduct maintenance.
Oil prices were also supported as the dollar declined from an eight-day peak. The Japanese yen rose as increased financial market volatility sent traders looking for a safe haven.
A weaker dollar makes oil and other dollar-denominated commodities cheaper for holders of other currencies.
The correlation between moves in the oil price and the dollar has strengthened in recent weeks, as investors increasingly sell other assets to buy the U.S. currency on expectations of a faster pace of rate rises.
Additional reporting by Amanda Cooper in London