The European Central Bank (ECB), led by Mario Draghi, came under pressure to act after inflation sunk to 0.3% last month.
Meanwhile, growth across the 18-nation bloc had ground to a halt in the second quarter as fears over the Ukraine crisis hit confidence.
The ECB had already cut interest rates from 0.25% to 0.15% in June but has now decided that even stronger medicine is needed, as it cut growth forecasts for this year and next.
It also cut the overnight deposit rate for lenders that hold money with it to -0.2% - a rate that had already been slashed below zero to -0.1%.
Mr Draghi said that in addition, the bank would start a new stimulus programme buying asset-backed securities.
The decision saw the euro plunge by nearly 1% against the US dollar while sterling climbed a cent against the single currency.
It came as the Bank of England left interest rates on hold at the UK's "emergency" rate of 0.5% and kept the quantitative easing scheme pumping £375 billion into the economy at the same level, despite the UK's accelerating growth.
Two members of the Bank's Monetary Policy Committee (MPC) have already voted to start raising rates, with the risk of growth bringing inflationary pressures further down the track in mind.
But the eurozone's woes are likely to have been among the risk factors cited by those arguing in favour of leaving them on hold at 0.5% - with the eurozone the UK's biggest trading partner.
Expectations of the timing of a UK hike have been dampened by weak wage growth - now seen as a central factor in rates decisions by the bank - with next February now seen as the most likely date.
A rise would put pressure on household finances, with a 0.25% hike likely to translate to an annual increase of £250 on a typical mortgage, though it would offer a fillip to savers who have been hammered by 0.5% rates since early 2009.
Martin Beck, senior economic adviser to the EY ITEM Club, said: "The case for leaving rates on hold for a few more months hasn't lost its strength.
"If anything, following today's decision by the ECB to cut borrowing costs, it has arguably been reinforced."
Howard Archer, chief UK and European economist at IHS Global Insight, said the ECB move showed just how worried it was about the economy.
"Until very recently, the ECB had seemed minded to hold off from taking any further stimulative action before the end of 2014," he said.
"However, the ECB's hand has clearly been forced by a further fall in eurozone consumer price inflation to just 0.3% in August, weakening inflation expectations and evidence that already weak eurozone economic activity was faltering."