To help fix the banks, the ECB will need to complete a yearlong review of their balance sheets to reveal hidden weaknesses and strengthen their finances.
But those steps will take months, if not years, to have an effect. With its rate cut, the ECB did what it could to show it is ready to support the economy now.
On Thursday, Draghi and the bank's governing council were responding in particular to an alarming drop in inflation, to just 0.7 percent in October. The rate is far below the ECB's inflation target of 2 percent and a sign of weak demand in the economy.
Low inflation is not itself a disaster. But it's a nightmare if it turns into outright deflation, an economic death spiral in which a chronic, broad-based fall in prices keeps people from spending as goods get ever cheaper. That's what happened in Japan, causing the country years of economic stagnation.
The rate cut highlights the diverging fortunes of the economies of Europe and the U.S., where the recovery has been stronger and the Federal Reserve is preparing to tighten its monetary policy.
Marie Diron, senior adviser to Ernst & Young's, said the direct impact of the ECB's rate cut will be limited. But that needs to be measured against the cost of inaction.
"No response to such low inflation would have been potentially very damaging as it could have sent the euro exchange rate higher," she said.
A stronger euro not only hurts European growth by making exports more expensive but also pushes inflation down further by making imports less expensive, increasing the risk of deflation.
The immediate benefit of Thursday's cut was evident in a drop in the euro. Startled currency traders sent its exchange rate down 2 cents against the dollar after the decision, to around $1.33.
The bank's willingness to move without waiting to tip markets ahead of time could enhance its credibility as the eurozone institution most able to act decisively, some economists said.
That was the role Draghi staked out in July 2012, when he promised to "do whatever it takes" to rescue the euro. He followed up with a plan to buy government debt that quickly calmed market turmoil in bond markets. It boosted investors' belief that Spain and Italy would not be allowed to default on their debts, a disaster that could have broken up the currency union.
Richard Barwell, an analyst at Royal Bank of Scotland, said that "failure to act would have entrenched perceptions that the council is impassive in the face of a weakening economic outlook."
The ECB will face pressure to take more steps and run the risks that come with them.
Diron and other economists think it will have to launch another offer of long-term, cheap loans to banks. Earlier such loans in 2011 and 2012 helped steady the banks, but did not result in much new lending to companies. Instead, some banks bought government bonds, tying their fate even more closely to troubled governments.
What the ECB has so far been unwilling to do is pump newly created money into the financial system, as the Fed, Bank of England, and Bank of Japan have done. Analysts say that might be too complicated, as the central bank oversees 17 different countries and bond markets.
Draghi said little about the possibility of such U.S.-style bond purchases, leaving open what the next move might be.
"There is a whole range of instruments that we can...activate if needed," he said.