Luxury condominium buildings on Fan Pier in Boston's Seaport District. iStock photo

As luxury home prices surged across the nation, even greater price appreciation was seen in Greater Boston.

The median sale price of the Boston area’s luxury homes increased on by 5.9 percent a year-over-year basis to $2,724,647 according to a new Redfin analysis. Luxury homes are defined as those estimated to be in the top 5 percent of their respective metro area based on prices of homes sold over a rolling 12-month period.

“Luxury buyers are still able to move forward in ways that many typical buyers can’t right now, whether that’s because they’re paying in cash, benefiting from stock-market gains, or taking out smaller loans,” Redfin Senior Economist Sheharyar Bokhari said in a statement. “Those advantages make them less sensitive to high mortgage rates, which helps keep demand at the top of the market steadier. In contrast, a lot of middle-income buyers are holding off until monthly payments come down or their financial outlook improves.”

Across the nation, the price of luxury homes rose by 5.5 percent year over year to a median $1,278,950, a record high for October. Luxury sales rose most in Nashville, Tennessee (20.3 percent), Kansas City, Missouri (16.5 percent) and Riverside, California (16.4 percent).

Additionally, sales activity increased across the nation and in Greater Boston. In that region, the number of luxury homes sold increased by 6.7 percent year-over-year, while the number of pending sales increased by 3.2 percent. That increase in sales came after a spring market that saw a build-up of inventory in the luxury market.

In the United States as a whole, luxury home sales increased by 2.9 percent year over year, and pending sales rose 2.1 percent for luxury homes