Dan Hipkiss' last-minute try delivered Leicester a remarkable comeback win in a controversial Heineken Cup clash.
Ospreys (10) 15
Tries: Williams, Connor
Leicester (3) 17
Tries: Lloyd, Hipkiss
Cons: Goode 2
The Ospreys' forward dominance set the way for Barry Williams and Shaun Connor tries, and with the Tigers down to 13 men at one stage a home win beckoned.
But poor kicking cost them as Leon Lloyd hit back, before Tom Varndell sparked the superb late Hipkiss strike.
Harry Ellis suffered a knee injury in an off-the-ball clash with Ian Evans that could threaten his England hopes.
That was far from the only controversial incident at the Liberty Stadium, with tensions running high from the previous week's game where the Tigers had been accused of cheating.
The result sends Leicester to the top of pool three ahead of Stade Francais, but ends the Ospreys' quarter-final hopes.
After a promising start by the Celtic League champions in Swansea, Connor missed a simple early penalty.
The fly-half then landed a more difficult shot before the inevitable first instance of Gavin Henson controversy.
An off-the-ball clash with Alejandro Moreno ended with the Tigers prop leaving the field streaming blood, Henson's boot appearing to catch the Italian's face.
Leicester equalised with an Andy Goode penalty, but the Tigers were struggling for a set-piece platform as the Ospreys disrupted their scrum and line-out.
The niggle increased as Ospreys lock Evans aimed a sly kick at Ellis, the scrum-half being forced off with a serious-looking injury that could rule him out of the Six Nations.
Connor missed another sitter of a penalty as half-time approached, and the poor kicking meant the Ospreys chose to punt their next penalty to touch.
The decision paid off as James Bater won the line-out, drove well, and found Evans who was held up inches short.
The ball was recycled and Jason Spice fed captain Williams, who burrowed in under the posts.
If the Tigers hoped the Ospreys forwards would tire after the break they were disappointed as the Welsh side produced a series of devastating scrum drives.
As the pressure built, Ollie Smith was sin-binned for killing the ball at the ruck.
Connor caught the Tigers defence napping with a quick tap and go, and had the pace to nip in at the corner for the second try.
Lloyd's try set up the Tigers fightback
The Tigers were down to 13 men when substitute Louis Deacon saw yellow for another offside offence.
The Ospreys attacked and Martin Corry was fortunate not to join his two team-mates in the bin as he killed the ball on his own try line.
The home side went for a series of short-range scrums, but Leicester somehow held out under enormous pressure - and then mounted a fightback.
From rare quality line-out ball they moved the ball smoothly across field to Leon Lloyd, the winger brushing aside a weak Adrian Cashmore tackle for a score converted superbly by Goode.
The Ospreys rallied, but Henson missed an easy penalty that would have taken his side two scores clear.
They still seemed safe, but a final, desperate Tigers attack swung from one side of the pitch to another before somehow finding Varndell deep in his own 22.
The lightning wing broke into the Ospreys half before being hauled down, but the attack continued and the recycled ball found substitute Hipkiss.
He found the gap in the splintered defence to cross under the posts, Goode adding the simple conversion for the win.
Ospreys coach Lyn Jones:
"We shouldn't have been in that position at the end, but we didn't put our kicks over or take our chances.
"I expected a bonus point win when they were down to 13 men and we were scrummaging on their line.
"We were about two seconds from a penalty try after a number of re-set scrums.
"We looked the better team for about 83 minutes, but Leicester showed their experience, did a lot of talking to the referee and influenced him.
"I can't comment on the Gavin Henson incident because I didn't see it, but last week he had his head stamped on and there was no citing so I don't foresee repercussions."
Tigers coach Pat Howard:
"Some may argue that the Ospreys were the better team on the day and we respect them, but it was two tries apiece, we took our opportunities and won the game.
"The players' commitment and ability to play a full 80 minutes was fantastic.
"At 15-3 down I thought we were in trouble, but a great captain [Martin Corry] brings people together.
"We're elated to be top of the group, but it's not signed, sealed and delivered yet.
"I won't comment on the Gavin Henson or Ian Evans incidents until I see the video."
Ospreys: Cashmore, Terblanche, Parker, Henson, Mustoe, Connor, Spice, D. Jones, B. Williams, A. Jones, Newman, Evans, Bater, Thomas, Tandy.
Replacements: A. Bishop for Connor (72), Bateman for Evans (80). Not Used: Bennett, Millward, Beech, M. Jones, S. Williams.
Leicester: Murphy, Lloyd, Smith, Cornwell, Varndell, Goode, Ellis, Moreno, Chuter, Morris, Cullen, Kay, B. Deacon, Jennings, Corry.
Replacements: Vesty for Murphy (75), Hipkiss for Cornwell (48), Healey for Ellis (36), Rowntree for Morris (51), L. Deacon for Kay (54), Abraham for B. Deacon (67). Not Used: Buckland.
Sin Bin: Smith (49), L. Deacon (57).
Referee: Alain Rolland (Ireland)