* 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 (Reuters) - Global equity markets and oil prices bounced back on Tuesday after data for January on business activity in the euro zone showed signs of recovery while the U.S. service sector grew last month for a third year of back-to-back monthly expansion. Wall Street followed the equity rally in Europe, opening higher, with major U.S. and European stock indexes up almost 0.7 percent or more. A measure of world equity markets also was higher, though not nearly as much. U.S. stocks advanced, fueled by strong fourth-quarter earnings and signs of improving economic growth, which suggested the longer-term trend for equities remains higher. "Stocks are really the only place investors can go for any kind of real return, and that's enough to have people continuing to come into the market, not just buying on dips but in general," said Thomas Nyheim, a portfolio manager at Christiana Trust in Greenville, Delaware. The Dow Jones industrial average was up 102.79 points, or 0.74 percent, at 13,982.87. The Standard & Poor's 500 Index was up 12.21 points, or 0.82 percent, at 1,507.92. The Nasdaq Composite Index was up 24.47 points, or 0.78 percent, at 3,155.64. 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 13/32, the yield at 2.0034 percent. 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. Brent crude oil rose over $1 a barrel to $116.87, while U.S. crude futures gained 79 cents to $96.96. "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 0.03 percent to trade at $1.3517.