Each of the two companies shipped 74.5 million smartphones in the October-December period, Strategy Analytics (SA) said.
But Apple did better than Samsung. The former's market share rose by two percentage points to a record 19.6 percent in the fourth quarter from a year earlier, while Samsung saw its share plunge by 10 percentage points to 19.6 percent, SA said.
Market watchers attributed Apple's Q4 robust sales performance largely to the popularity of its new iPhone 6 and 6 Plus models in China, the United States and Europe.
"Samsung continues to face intense competition from Apple at the higher-end of the smartphone market, from Huawei in the middle-tiers, and from Xiaomi and others at the entry-level," SA said.
"Samsung may soon have to consider taking over rivals, such as BlackBerry, in order to revitalize growth this year," it said. Earlier this month, Samsung denied media reports that it had offered to buy the Canadian smartphone maker for as much as $7.5 billion.
Lenovo-Motorola ranked third with 24.7 million smartphones, or 6.5 percent of the market, shipped, followed by Huawei (24.1 million units, or 6.3 percent).
Global smartphone shipments reached a record 380 million units in the fourth quarter last year, up 31 percent from a year earlier, the market researcher said.
Samsung remained the No. 1 smartphone player globally on a full-year basis in 2014, SA said.