Scott Johnson’s men finished the pool stages as one of the two best runners up after Clermont Auvergne’s bonus-point win in Viadana secured top spot for the French side.
A single try from Tommy Bowe, together with four penalties from the boot of Dan Biggar, was enough to see the Ospreys triumph at the Liberty Stadium as they made it four wins from six in Pool 3.
Leicester’s exit means they fail to qualify for the quarter-final stages for just the fourth time in 13 seasons, eight months after they narrowly missed out on a third European crown with defeat to Leinster in last year’s Murrayfield final.
Their demise also leaves England with their lowest-ever number of clubs in the last eight, with only Northampton Saints and London Irish still in with a chance of obtaining the continent’s Holy Grail prior to this evening’s late kick offs.
A hard-fought first 35 minutes swung one-way then the other, as both sides turned possession into points but only through the boot.
Toby Flood opened the scoring for the visitors with just five minutes on the clock but Biggar knocked over a short-range drop goal to bring the Ospreys level four minutes later.
A second Flood penalty re-established Leicester’s three-point advantage with 11 minutes played but the Ospreys again hit back through Biggar just three minutes later.
Jeremey Staunton’s 22nd minute drop goal was matched by Biggar’s third consecutive penalty before the Liberty Stadium erupted as the Ospreys crossed for the opening try of the game four minutes before half-time.
A fine piece of individual skill from James Hook paved the way for Bowe to complete a personal milestone of a try in all six group games in Europe’s premier club competition.
Hook’s delicate left-footed grubber kick beat the turning Leicester defence and fell perfectly for the onrushing Bowe who touched down in the far left-hand corner.
Referee Alan Lewis requested confirmation from the television match official but the try never looked in doubt.
Biggar was off target with the difficult conversion attempt but the Ospreys were now in possession of a five-point lead at 14-9.
A flying-arm tackle from Ospreys scrum-half Ricky Januarie on opposite number Ben Youngs gave Flood the chance to narrow the gap on the stroke of half-time but the England international sent his 35-metre attempt wide of the near post.
Biggar should have moved the home side two scores clear just two minutes after the restart but he failed with a 35-metre penalty attempt of his own from straight in front of the posts.
The young fly-half then followed Lee Byrne in missing a drop goal a minute later, with the Tigers breathing a sigh of relief to stay within five points of the Welsh region.
Flood and Biggar then swapped penalties after 50 and 54 minutes respectively but possession and territory was beginning to swing further and further in the Ospreys’ favour.
But just as it looked as if the Ospreys were growing into their 17-12 advantage, Leicester began to turn the screw as they went looking for the try that would give them at least a draw and therefore almost certainly guarantee their own passage into the knockout stages.
The 2001 and 2002 Champions went close on a number of occasions, most notably when Lewis Moody surged towards the Ospreys line only for Heineken Man of the Match Marty Holah to somehow drag the England flanker down by nothing more than his shirt tails.
Even with time fast running out, the Tigers still came close to stealing what would have been a famous away victory.
Leicester pressed and pressed in the closing stages, with phase after phase of possession rocking the Liberty Stadium faithful with just a minute left on the clock.
But the Tigers’ European dream effectively came to an abrupt end when former All Black Aaron Mauger knocked on following a poor pass from Youngs just five metres out.
The Ospreys now face an away trip to one of the top two seeds in early April, while Leicester will have to wait at least another season to repeat the glories of 2001 and 2002.
