There were limited chances until Borriello volleyed in a corner from in front of goal.
''Both teams played with young players,'' Roma coach Rudi Garcia said via a translator. ''I am quite happy with the development we had.''
For the second time in three years, Fenway, the home of the Boston Red Sox, was transformed into the home of Liverpool, which is owned by Fenway Sports Group. John Henry, owner of the Red Sox, also is the controlling partner of Fenway Sports Group.
Roma beat Liverpool 2-1 at Fenway two years ago.
''It's the second time in the last couple of years,'' Liverpool coach Brendan Rodgers said. ''It was a great atmosphere. The support was great. I think it was for both - fantastic. For a preseason game, it was a very, very good game.''
Roma is by NBA team, the Boston Celtics, minority owner Jim Pallotta.
Roma goalkeeper Lukasz Skorupski made a diving save near the post on Rickie Lambert's kick from just outside the box in the 57th minute.
Roma seemed to have the territorial edge in the first half and Liverpool a slight edge in the second in a match that had just a handful of shots on goal.
Liverpool rested a number of its star players, including captain Steven Gerrard, but the mostly red-clad crowd didn't seem to mind.
''It's going to be great for me to see our young players gain experience,'' Rodgers said.
Wednesday's game was the first of four scheduled matches in the United States for Liverpool, which travels to Chicago, New York and Charlotte.