The official data prompted the government to upgrade growth forecasts for the second time in a week and to promise no new austerity measures.
Last week, growth for 2014 was up-rated to 3% from 2.1%, but will now be around 4.5%, Ireland's finance minister said.
Michael Noonan said the economy was in "a catch-up phase... after recession".
The year-on-year growth of 7.7% was the strongest recorded in Ireland since the early 2000s, Mr Noonan told reporters. By comparison, the eurozone recorded growth of just 0.7% over the same period.
Along with Greece, Spain and Portugal, Ireland was among the eurozone's worst hit economies, with the bursting of its property bubble and soaring unemployment.
The 1.5% quarterly rise beat the 0.5% expected by economists polled in a survey by the Reuters news agency.
Mr Noonan said the faster growth would mean Ireland's budget deficit falling to about 3.5% of GDP this year against a target of 4.8%. That meant 2bn euros of tax rises and spending cuts planned for next year would no longer be needed to reach the EU limit of 3% by the end of 2015, he said.
The economic improvement comes after years of austerity, a bailout from international lenders, and relentless austerity measures.
"At face value, the numbers suggest that the boom is back," said Austin Hughes, chief economist at KBC Bank Ireland.
"It shows a clearly improving economy. It's very encouraging to see the improvement in consumption, in construction. So a domestic recovery is taking hold, if a lot less intense that the headline number would suggest," he said.
The Republic of Ireland's economy grew 1.5% in the second quarter of the year, figures show, and was up 7.7% on the April-to-June period in 2013.