More homeowners in the Boston area are coming up for air. A new report from the real estate firm Zillow Inc. shows 122,653 borrowers—or 15 percent—were “underwater” on their mortgages in the second quarter, meaning they owed more to lenders than their homes were worth. That was down from 15.9 percent in the first quarter of 2013 and 19.6 percent during the second quarter of last year. The improvement, while modest, is another sign of the region’s rejuvenated real estate market.

Community-by-community, so-called “negative equity” rates vary widely. In the second quarter, Brockton had the highest percentage of underwater homes with 42.3 percent, while Wellesley’s rate of 3.3 percent was the lowest.

Zillow also reported that among the 30 largest metro areas it keeps tabs on nationwide, Boston had the third-lowest level of negative equity for the second quarter.

Advertisement - Continue Reading Below

The company said it expects the region’s underwater rate to keep dropping into next year. By the second quarter of 2014, it said, the percentage of Boston-area homes valued at less than what is owed lenders will decline to 13.4 percent or lower, according to Zillow. That translates into about 13,300 more Massachusetts homeowners who will start to build equity in their properties after sweating out a long and painful downturn in values.