The victory - with a bonus point to boot - puts the Welsh region right back in the frame for qualification from Pool Four. They now have two mammoth games left before them - away to Munster then home to Castres - before they can even think about reaching the last eight.
Springbok Terblanche got the Ospreys off to a flying start with an early try that stunned the majority of the near 8,000 crowd in west London. The Ospreys travelling support may have been outnumbered but - like their team - made their presence felt and their joy soon turned to elation when Henson got his first.
It came from a stunning team move started from centre partner Sonny Parker. His scorching break through the middle was closely supported by Jason Spice before replacement hooker Mefin Davies was tackled just short. The Ospreys recycled quickly, Mathew Jones delivering the killer pass for Henson to glide over.
England World Cup star Will Greenwood hit back from close range minutes later to steal back the lead for Harlequins. But then the powerful Ryan Jones picked up from the base of a scrum and picked a clear path to the try line as Quins were left scratching their heads. Henson converted for a 22-16 half-time lead.
After a nervy start to the second half, the Ospreys backs found their groove again and hit their hosts with three hand-crafted. Henson showed his class and a killer finishing touch to score the fourth, Williams latched onto Mathew Jones' kick ahead before the young outside-half got the try he deserved right at the end.