* Dollar surges on U.S. job growth, wages increase
* U.S. crude ends lower on week, speculators cut long positions
* U.S. output exceeded 10 mln bpd in November, first since 1970 (Updates with settlement prices, updates bullet points, adds additional quotes, details of futures positions)
NEW YORK, Feb 2 (Reuters) - Oil prices fell on Friday as the dollar surged following strong U.S. jobs numbers, though compliance with output cuts by OPEC and rising global demand kept much of the early year oil rally in place.
An increasingly correlated trade between oil, stocks, bonds and the dollar has amplified swings in the markets.
U.S. West Texas Intermediate (WTI) crude settled down 35 cents to $65.45 a barrel, after earlier losing more than 1 percent. Brent lost $1.07, or 1.5 percent, to $68.58 a barrel. The deep decline in Brent narrowed the gap between it and WTI to its narrowest since August; that wide gap has boosted U.S. exports in recent months.
Oil fell as the dollar rose after U.S. jobs growth surged in January and wages rose, recording their largest annual gain in more than 8-1/2 years.
The market this week has had a strong tie with the dollar. When the dollar basically bounced, we had to start selling," said Gene McGillian, manager of market research at Tradition Energy in Stamford, Connecticut.
The once-strong connection, where oil rises when the dollar falls and vice versa, ebbed between 2014 and 2016 during a three-year supply glut.
With supply tightening, the relationship has reasserted itself. Since the beginning of the year, oil and the U.S. dollar index have had a correlation of -0.86, with -1 being a perfectly inverse relationship.
Futures positioning from the Commodity Futures Trading Commission showed speculators reduced their positions in crude oil futures, though speculators still have a long position of 531,235 contracts, as they have been buying heavily in recent weeks during the oil market rally.
McGillian said support from buyers will diminish if the coming weeks show additional increases in crude inventories after this week's data showed the first build after 10 weeks of declines.
"If we see refinery rates down that could be the spark that sets up some profit-taking and we could see a correction," he said.
U.S. crude stocks rose by 6.8 million barrels for the week ended Jan. 26. Output cuts from large producers, strong demand and declining imports has helped draw down U.S. supply.
"Demand has quietly underpinned the tightening of the market over the past year," said Jon Rigby, UBS analyst, in a note.
January production from the Organization of the Petroleum Exporting Countries rose from an eight-month low, according to a Reuters survey. Russian data showed strong compliance with output cuts, even as production hit 10.95 million bpd.
The cuts have offset gains in U.S. crude production. U.S. output surpassed 10 million bpd in November for the first time since 1970, the Energy Information Administration said this week.
For the week to Feb. 2, Baker Hughes said drillers added six rigs to bring the overall count to 765, the second straight week of gains.
(Additional reporting by Dmitry Zhdannikov, Henning Gloystein and Aaron Sheldrick; Editing by David Gregorio and Lisa Shumaker)