Late show Ospreys stun Tigers to advance in Champions Cup
Reduced to 14 men after a yellow card for replacement prop Dan Richardson, two-time European champions Leicester were unable to hold back the Welsh side's surge with backrower Jac Morgan scoring from close range.
Owen Williams then held his nerve to kick the winning conversion.
"When the draw was made, most people would have thought that the later rounds in April and May wouldn't concern us," said Ospreys coach Toby Booth whose side ended the pool stage with three wins from four games.
Two of those victories came against French champions Montpellier.
Leicester had already secured qualification for the knockout rounds before seeing their 100% winning record end.
"We are desperately disappointed as the defeat was by our own making as we opened the door for them and they are a good side in great form," said Leicester coach Richard Wigglesworth.
"But we are through to the knockout stages and we would have taken that outcome before the competition started."
Jack van Poortvliet and Harry Simmons scored Leicester's tries, with Springboks star Handre Pollard converting both and adding four penalties.
Dewi Lake, Keelan Giles and Morgan crossed for the Ospreys. Williams kicked two penalties and two conversions with Cai Evans adding a conversion.
After three defeats to start the competition, French side Lyon kept alive their slim hopes of making it to the last 16 by defeating South Africa's Bulls 31-7.
Hooker Guillaume Marchand, with two tries, and scrum-half Jean-Marc Doussain scored in the first half for Lyon and a 24-0 interval lead.
Kurt-Lee Arendse reduced the arrears for the Bulls with their only try before fly-half Leo Berdeu grabbed Lyon's fourth score just before the hour mark to secure a bonus point.
Bulls have yet to make sure of their place in the last 16 while Lyon appear destined to drop into the knockout rounds of the Challenge Cup which they won last season.
"Few people saw us qualifying with a victory against the Bulls," said Berdeu.
"It doesn't matter if we return to the Challenge Cup. If we go down to that level, we will be keen to defend the title we won last year."
