The Aussie, which is often used as a more liquid proxy for Chinese investments, rose more than 1 percent to $0.8723 , with the rate cut likely to assuage fears of a Chinese slowdown that have hurt commodity currencies.
Draghi's comment that the ECB is ready to act in a timely manner if low inflation persists sparked talk of more measures as early as next month, and knocked the euro 1.7 percent lower against the Aussie to A$1.4284. It also drove down peripheral bond yields and bolstered European stocks.
Earlier, the yen charged higher after Japanese Finance Minister Taro Aso said the currency's fall over the past week was too rapid, one of the strongest warnings against a weak yen since Japan started its aggressive monetary stimulus in 2012.
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The dollar fell to 117.355 from around 118 yen before his comments. It was last at 117.75 yen, down 0.4 percent on the day, and below Thursday's seven-year high of 118.98 yen.
The dollar has climbed almost 10 yen since the Bank of Japan surprisingly eased policy in late October.
"Aso's comments are not very surprising given he is speaking about the rapid pace of the yen's fall," said Yujiro Goto, FX strategist at Nomura. "While the comments will slow the pace of yen depreciation, I don't think it will change the overall momentum. We can expect some consolidation here."
Traders said investors would look to rebuild long dollar/short yen positions if the pair drops towards 117 yen.
Sterling dipped to $1.5660 after UKIP took a second seat from the ruling Conservatives in a by-election after a Conservative lawmaker defected to the anti-EU party, underlining political risk in the run-up to next May's general election.