* Economic data fuels European, U.S. stock rally * World equity markets rebound from Monday's sharp sell-off * Euro lifted by above-forecast euro zone services data * Brent crude close to $117 a barrel By Herbert Lash NEW YORK, Feb 5 Global equity markets and oil prices bounced back on Tuesday after data showed the vast U.S. services sector extended a three-year expansion last month, while business activity in the euro zone showed signs of recovery. Major U.S. and European stock indexes rallied, with Wall Street gaining about 0.8 percent, after a sharp sell-off the previous session on renewed worries about the euro zone crisis. A measure of world equity markets also was higher, though only slightly as emerging market shares declined. U.S. and European stocks advanced, fueled by strong fourth-quarter earnings and signs of improving economic growth, which suggested the longer-term trend for equities remains higher. "Yesterday's spotlight on Southern Europe was just an excuse to book profits and catch our breath. The trend is still positive, and clients are slowly coming back to equities," said Patrice Peroise, a trader at Kepler Capital Markets. The Institute for Supply Management said its U.S. services sector index eased slightly, to 55.2 last month from 55.7 in December. The reading was in line with economists' forecasts, according to a Reuters survey. Tuesday's data bolstered the view that the world economy was improving, a sentiment that has lifted stock markets around the globe and pushed the benchmark U.S. S&P 500 to five-year highs. In the biggest leveraged buyout since the financial crisis, Michael Dell reached a deal to take computer maker Dell Inc private for $24.4 billion. The move will allow the billionaire chief executive to try to revive the fortunes of his company without Wall Street scrutiny. Corporate results also helped the rally. With 56 percent of S&P 500 companies reporting, 68.7 percent posted earnings that beat expectations, or better than the 65 percent rate over the past four quarters or the 62 percent pace since 1994. The Dow Jones industrial average was up 105.14 points, or 0.76 percent, at 13,985.22. The Standard & Poor's 500 Index was up 12.68 points, or 0.85 percent, at 1,508.39. The Nasdaq Composite Index was up 30.72 points, or 0.98 percent, at 3,161.88. MSCI's all-country world equity index rose 0.2 percent to 354.77, while the FTSEurofirst 300 index of top European shares closed up a provisional 0.3 percent at 1154.47. U.S. Treasuries prices fell, spurred by Markit's Eurozone Composite PMI, which rose to a 10-month high of 48.6 from 47.2 in December - better than the preliminary reading of 48.2. The data is based on business activity across thousands of companies and is considered a good gauge of growth. The benchmark 10-year U.S. Treasury note was down 14/32 in price to yield 2.0052 percent. Brent crude oil rose $1.32 a barrel to $116.92, while U.S. crude futures gained 63 cents to $96.80. "We do not envisage prices receding for any great length of time," said Carsten Fritsch, an analyst at Commerzbank. "The supply-side risks still prevailing, shrinking OPEC supplies and the brightening global economic outlook all suggest that such a retreat is unlikely." The euro rose against the dollar and yen, returning to its months-long trend of appreciation, as better-than-expected euro zone data affirmed expectations that the European Central Bank will keep policy steady when it meets this week. The euro, which had taken the brunt of the selling and fallen from a high of over $1.37 at the end of last week to under $1.35 on Monday, rose 0.39 percent to trade at $1.3566.