In the 27-member EU, industrial production was up 0.9 percent in March, again compared with 0.3 percent the previous month, the Eurostat data agency said.
The biggest monthly gains were in bailed-out Portugal, up 5.3 percent and the Netherlands, up 4.5 percent, with Slovenia seeing the largest fall at 2.9 percent.
Compared with output in March 2012, eurozone industrial output was down 1.7 percent, with the wider EU dropping 1.1 percent, Eurostat said. In February, these readings showed falls of 3.2 percent and 2.6 percent, respectively.On this annual basis, Luxembourg was the biggest loser, down 6.9 percent, followed by Italy, 5.2 percent, and Ireland on 4.1 percent while the Netherlands gained 11.1 percent.
Analysts said the March report was surprisingly strong but did not necessarily mean that the worst of the eurozone's long recession is over.
Howard Archer at IHS Global Insight said the outcome would bolster overall eurozone growth figures for the first quarter to still leave them in negative territory but much better than the fourth quarter slump of 0.6 percent.
"Although significantly better than expected, it should be noted that eurozone industrial production was lifted in March by a sharp jump in energy output which was undoubtedly lifted by unseasonably cold weather in many countries," Archer noted.
"While the March industrial production data are relatively encouraging, the Eurozone manufacturing sector is very far from out of the woods.
"Eurozone manufacturers currently still face a daunting domestic and global economic environment, which will make it hard for them to build on March's unexpectedly decent industrial production rise," he said.