The 13-country area's economy grew 3.1% year-on-year - below the 3.3% growth seen in the previous quarter, but beating the 2.9% forecast.
The data fuels analysts' view that the area's interest rates are set to rise.
Last week, the European Central Bank (ECB) kept rates at 3.75%, but the bank's head called for "strong vigilance" to counter price risks.
The expression by Jean-Claude Trichet is viewed as a way of implying that the benchmark rate will be lifted to 4% at the ECB's next meeting in June.
"Stronger-than-expected eurozone GDP growth should help provide the extra leverage to the ECB for higher rates in the next few months," said David Brown of Bear Stearns.
While annual growth was 3.1%, growth on a quarter-by-quarter basis hit 0.6%, beating the 0.5% forecast.
"Today's GDP [gross domestic product] report strengthens our belief that the eurozone economy is on a sustained growth trajectory," said Martin van Vliet, an economist at ING.
A major factor behind the growth was strength in Germany -
Separate data from Germany's government showed that national growth for the quarter - while less than the previous period - beat expectations, hitting 0.5%.
Although German consumer spending was dented by higher value-added tax (VAT), which rose from 16% to 19% in January, this was countered by strong investment.
Economists greeted the German figures - which showed a 3.3% rise year-on-year - positively.
Bear Stearns' David Brown said: "With the impact of Germany's VAT hike causing less damage to German growth in the first quarter, it has helped solidify euro zone growth... over the last 12 months."
Sebastian Wanke of Dekabank said: "Although the basic story of private consumption and trade as brakes on growth... appears to be valid, it is happening at a higher level than expected."
Meanwhile, official data from France showed its economy grew by 0.5% in the quarter - the same as the previous three-month period.
Overall, the 27-member European Union saw growth reach 3.2% year-on-year, exceeding the 2.1% seen in the US for the same period.
Separately, the European Commission forecast strong growth over the next six months in the eurozone, before slowing in the final quarter.