Harlequins (3) 8
Henson gave the Ospreys a second successive semi-final place
Ospreys (6) 19
Pens: Henson (4)
The Ospreys ensured Wales have a representative in the EDF Energy Cup semi-finals after beating the Harlequins in a poor game at the Stoop.
Gavin Henson scored all the Ospreys' points with two penalties in each half and a late intercepted try.
The visitors had three men in the sin bin at the end of the first half, but the Quins failed to score any points.
De Wet Barry's second-half try, adding to Adrian Jarvis' first-half penalty, proved far too little for the Quins.
They wasted a magnificent opportunity to stamp their authority on the match when the Ospreys had prop Paul James, full-back Lee Byrne and fly-half Henson in the sin bin.
But a combination of clueless Harlequins play and defensive resilience saw the Ospreys hold out and go into the break 6-3 up thanks to Henson's two penalties.
The visitors were fortunate not to be penalised for a penalty try, though, when hooker Huw Bennett blatantly pulled back Quins flanker Chris Robshaw as he chased a kick ahead over the Ospreys tryline.
But just as the Ospreys were set to return to their full complement of 15 men, centre Barry crossed for the Quins.
Jarvis' chip ahead found a gaping hole behind the Ospreys defence, and Barry comfortably won the race to ground the ball.
Jarvis missed the conversion and so the home side's lead lasted all of two minutes as Henson put the Ospreys back in front with a third sweetly struck penalty.
The remaining 20 minutes were largely forgettable as both sides were guilty of poor discipline and even worse handling.
Harlequins played the final seven minutes with 14 men as Barry became the fourth player to receive a yellow card, Henson adding another three points from the resulting penalty.
Henson, playing at fly-half in James Hook's absence due to injury, then wrapped up the victory in injury time when he intercepted a long Quins pass to score under the posts and then added the conversion.
Harlequins director of rugby Dean Richards:
"I never criticise referees so I shouldn't start now, but he should have given the penalty try.
"We will monitor the video and if there are any comments to be made we will go through the official channels."
Ospreys coach Lyn Jones on Henson's switch from centre to fly-half:
"Gavin was happy to do it. He was brought up at outside half and he's a good player.
"Gav's performances are improving. He has been in and out of rugby for two years since the Lions tour and other instances and he's got fit since being left out of the World Cup.
"His fitness has improved, his confidence has shot up and he's a different person at the moment."
Harlequins: Brown; Keogh, Strettle, Barry, Monye; Jarvis, Gomarsall; Jones, Fuga, Ross, Kohn, Spanghero, Robshaw, Skinner, Easter (capt).
Replacements: Turner-Hall for Jarvis (75), So'oialo for Gomarsall (52), Botha for Fuga (52), Evans for Spanghero (52).
Not Used: Nebbitt, Hala'ufia, Williams.
Sin Bin: Barry (73).
Ospreys: Byrne, Walker, Taylor, Parker, S. Williams, Henson, Phillips, James, Bennett, A. Jones, Wyn Jones, Evans, T-Pole, Holah, Thomas (capt).
Replacements: Hibbard for Bennett (69), Millward for A. Jones (68), D. Jones for T-Pole (37).
Not Used: Bateman, Lewis, Wells, Connor.
Sin Bin: James (26), Byrne (30), Henson (35).
Ref: Hugh Watkins (Wales).