The Rockets didn’t score a point in today’s playoff game against the Lakers until about 5 minutes 15 seconds had passed in the first quarter. They didn’t score a field goal until more than 7 minutes 15 seconds had passed.
Are these records for the playoffs?
IIRC there’s been instances of teams scoring 4 points in a quarter. The “record” may be lower than that (for either regular season or post-).
I would reckon they are not records. It may seem ridiculous, but it really isn’t that ridiculous—comparatively.
Lakers 40, Kings 4 (after 1st quarter).
No field goals, ties record for fewest points in a quarter. Wasn’t playoffs and not sure if the record has been broken since.
I’m going to go out on a limb and suggest that the Kings didn’t make the playoffs at all that season. 
Based on that quarter’s performance, I wonder if they won a game. Granted they were in The Forum with Magic, Kareem, Worthy, Scott, Cooper, Green, etc.