Toyota's gains last month came on record sales of its RAV4 compact crossover, which rose 25 percent to 34,120, and the midsize Highlander, which jumped 28 percent. Sales of the 4Runner SUV rose 24 percent.
The C-HR, which went on sale in April, tallied 3,100 sales. Prior to its debut, Toyota did not have a subcompact crossover, an increasingly popular segment.
In pickups, the midsize Tacoma rose 4 percent last month, while the full-size Tundra gained 4.3 percent.
Toyota's car sales held up relatively well given the broad shift in the market, with the Corolla sedan falling 4.9 percent and the outgoing Camry down 9.5 percent.
That left the Camry, America's best-selling car for 15 years, again behind the Corolla in monthly sales.
In another sibling rivalry, the RAV4 outsold the Camry in the first half of the year, putting it on track to become Toyota's best-selling vehicle for the first time.
Over at Lexus, light trucks scored the only gains. Sales of the NX crossover rose 13 percent, and the bigger RX gained 4.5 percent. Sales of the LX large SUV rose 30 percent to 398 units.
The best-performing Lexus sedan last month was the ES, which fell 7.8 percent to 4,666 units. The low-volume RC coupe and GS sedan were down sharply.
The recently introduced LC 500 flagship coupe posted sales of 423 units in June and 845 year-to-date.
Incentive spending per unit at Toyota, including Lexus and Scion, rose 9.3 percent in June compared with the year-earlier month to $2,506, according to ALG. But that figure was down 3.3 percent from May, ALG said.