The US Commerce Department said strong consumer and government spending helped to bolster the economy.
But lower exports weighed on growth, after a surge earlier in the year as firms rushed shipments to beat tariffs.
The 3.5% gain marked a slowdown from the 4.2% pace in the second quarter, but was better than the 3.3% expansion economists had predicted.
“Growth downshifted a bit in Q3 and we look for some further slowing in the quarters ahead,” analysts at Wells Fargo wrote.
“That said, the US economy continues to grow in excess of the rate that most analysts consider to be its long-run potential growth rate.”
The US economy is expected to grow at about 3% in 2018 – which would be the fastest rate in more than a decade.
The pick-up comes as unemployment rates hover near record lows, and government policies, including a $1.5tr tax cut and expanded military budget, fuel spending.
In the third quarter, consumer spending – which accounts for more than two thirds of output – grew at an annual rate of 4%. That was up from a rate of 3.8% recorded in the previous quarter.
Overall, gross domestic product in the third quarter was up 3% compared to the same period in 2017.
But the Commerce Department report also contained signs that the environment for growth may be weakening.
Business investment increased at an annualised rate of less than 1%, while housing expenditures fell 4% – the third quarter in a row of contraction.
Exports of goods also fell by 7% in the three months to 30 September, after spiking 13.5% in the prior period.
The decline followed a wave of duties on American-made products that went into effect this summer, prompted by new US tariffs on foreign steel and aluminium, as well as billions of dollars worth of Chinese goods.
Kim Gittleson, New York business correspondent
A truism of American politics has long been that what matters most to voters is the economy.
If that’s the case, this report will give Republicans much to cheer.
Released just a little over a week before competitive midterm elections here, it gives President Trump’s party yet another data point to use as they try to convince voters that they’re responsible for the strongest economy in nearly a decade.
In particular, one of the key drivers of economic activity has been American consumers, who increased their spending by 4% over the past quarter. That surprised many, but it indicates that low unemployment, increasing wages and lower taxes have all helped to encourage Americans to shop.
The key question, of course, is if voters here believe that it is Republican policies that have powered this economic boom – and if that will be enough to help them keep control of Congress, even with a President whose divisive policies have turned this midterm election into more of a referendum on his personality instead of his party.