It follows four grim years in which activity troughed out last September at more than a quarter below the pre-recession peak.
As well as infrastructure work, the pick-up included a 6.2 per cent quarterly increase in residential building, led by Canterbury.
On the spending side of the accounts there was a 12.8 per cent jump in business investment in plant and machinery, lifting it to its highest in four years.
Household consumption, however, was subdued growing 0.2 per cent. The main driver was spending on durables such as cars, assisted by the strong dollar. Household spending on non-durable goods and on services was flat.
ANZ economist Mark Smith said the recovery had been tepid, with economic activity now just 2 per cent above its pre-recession level 4 years ago.