The German figures also provided more evidence of an emerging two-speed recovery across the 16-nation eurozone, however.
The Economy Ministry reported an estimated 2.9 percent monthly leap in output and said that while an upward trend seen earlier this year had slowed, it was still on track.
"The trend higher has slowed, as expected, from a strong first half, but it remains solid," a ministry statement said as the economy pursued a recovery from its worst post-war recession in 2008-2009.
Officials revised the decline in September industrial production to 1.0 percent from an initial estimate of 0.8 percent.
The news of October's rebound came after Europe's biggest economy reported a monthly drop of 1.1 percent in October exports, allowing economists to maintain forecasts for a solid end to the year.
"We should not count our chickens before they are hatched but these numbers promise another smashing quarter," ING senior economist Carsten Brzeski said.
With Germany already benefiting from a remarkable recovery in the first half of the year, the central bank expects full-year growth of 3.6 percent, which would mark the biggest jump since the country was reunified in 1990.
While the economies of Germany and other core eurozone countries are chugging ahead, partners on the bloc's periphery - notably Portugal, Spain, Greece and Ireland - are struggling with debt and deficit crises that have stymied growth.
Germany has blocked proposals for common eurozone bonds to provide cheaper funding for members with massive public deficits and debt, and on Wednesday, Jean-Claude Juncker, the Luxembourg prime minister, attacked Berlin for acting in an "un-European" manner.
A breakdown of the German ministry data showed that production of capital goods, those used to produce finished products, soared by 4.6 percent on the month, while intermediate goods posted a gain of 2.9 percent.
Output of finished consumer goods was up by a more modest 0.8 percent. Production in the energy sector fell by 0.3 percent, but it was a good month for construction, where activity expanded by 1.3 percent.
All of the main German industrial sectors had declined in September, but a two-month calculation designed to smooth out the data showed that output gained 1.1 percent in September and October compared with July-August.
In October, German industrial orders also rose 1.6 percent on the month, official data showed on Tuesday, a further positive sign for the last quarter of 2010.
"The implications for GDP (gross domestic product) growth in the fourth quarter are clearly positive," Capital Economics chief European economist Jonathan Loynes said.