According to this 49 points (one team) in a quarter in NBA finals is a record:
Finals Records: Points - Game
Most points, one quarter
Individual:
25 - Isiah Thomas, Detroit at L.A. Lakers, June 19, 1988
Team, first quarter:
43 - Philadelphia vs. San Francisco, April 14, 1967, Philadelphia at San Francisco, April 24, 1967
Both teams, first quarter:
84 - Philadelphia (43) at San Francisco (41), April 24, 1967
Team, second quarter:
46- Boston vs. St. Louis, March 27, 1960
Both teams, second quarter:
73 - St. Louis (38) vs. Boston (35), April 8, 1961, Boston (38) vs. Los Angeles (35), April 14, 1962
Team, third quarter:
47 - Los Angeles vs. Boston, June 3, 1984
Both teams, third quarter:
80 - Los Angeles (47) vs. Boston (33), June 3, 1984
Team, fourth quarter:
44 - Philadelphia vs. Los Angeles, June 6, 1982
Both teams, fourth quarter:
76 - Philadelphia (38) at Los Angeles (38), June 1, 1982
Team, overtime period:
22 - Los Angeles vs. New York, May 1, 1970
Both teams, overtime period:
38 - Los Angeles (22) vs. New York (16), May 1, 1970
http://www.nba.com/history/records/finals_game_points.html