South Korean-based Samsung remained the top vendor and China's Huawei held its number two spot despite US sanctions, ahead of third-place Apple, the research group said.
"Worldwide demand for smartphones is recovering, due to strong pricing competition among vendors and new innovations such as larger screens and 5G connectivity," said Linda Sui, an analyst with the group.
Samsung extended its lead in the market by boosting sales by eight percent in the quarter to 78 million units, representing a 21.3 percent share.
Huawei was the biggest surprise, showing a gain of 29 percent with 66 million units sold, giving it an 18.2 percent market share despite sanctions imposed by Washington that could make it harder to obtain key technology and components.
The Chinese firm, which launched its latest high-end smartphone in September without popular Google apps, picked up gains in its home market, according to Strategy Analytics.
It said Huawei's gains were largely in its home market.
The report said Apple's sales of iPhones fell three percent from a year ago to 45.6 million units, giving it 12.4 percent of the market.
Apple, which released its quarterly update Wednesday, did not disclose iPhone unit sales but said revenue from its iPhones was down nine percent.
The report showed China-based Xiaomi maintaining fourth place with a nine percent market share, followed by another Chinese firm Oppo, at eight percent.