Economists had expected the gross domestic product of the 18 countries that share the euro as currency to grow 0.2 percent after a 0.1 percent gain in the third quarter.
France provided some of the unexpected boost. The French economy also rose 0.3 percent in the October through December period, one tick faster than expected.
Germany's export-oriented GDP also beat expectations by one tick, coming in at a rate of 0.4 percent growth.
Eurostat said the economy in the larger 28-member European Union rose 0.4 percent in the fourth quarter after rising 0.3 percent in the third quarter.
While the fourth quarter figures are considered estimates that could be revised, Eurostat said the GDP fell 0.4 percent in the eurozone and rose by 0.1 percent in the EU over the whole year of 2013.
From the third quarter, the GDP dropped 1 percent in Cyprus and 0.8 percent in Finland. The one other country with negative growth in the quarter was a 0.1 percent drop posted by Estonia.
Romania topped the list among countries with available data, with growth reaching 1.7 percent. The Czech Republic notched growth of 1.6 percent quarter to quarter. Lithuania's growth was estimated at 1.2 percent.