Hampshire then lost their sixth wicket when Dimitri Mascarenhas (five) was caught off Harbhajan, and were soon eight down when Kumble removed Adrian Aymes (18) and James Hamblin in swift succession.
Quins fly-half Adrian Jarvis hit the crossbar from 30 metres soon after and the home side injected a bit of life into the game when England scrum-half Shaun Perry made a 25m jinking run.