Shane Williams led a remarkable comeback as the Welsh region recovered from 28-6 down to within a score in one of the greatest cup final turnarounds in history.
Lee Byrne and Nikki Walker also crossed as the Ospreys dug deep to recover from a nightmare first half, taking this second Anglo-Welsh to the wire.
In the end it was not enough to make up for the first forty minutes, in which Leicester crossed four times, as the Twickenham hoodoo struck Welsh hopes yet again.
Victory for Leicester keeps their hopes of a treble alive but there was concern at the final whistle for Wales star Ryan Jones who was carried off on a stretcher with a knee injury. It was a bitterly disappointing end given the excitement surrounding the Ospreys' first appearance in a major final.
The region had organised a convoy of 80 coaches to ferry supporters to Twickenham and it had looked promising after they got the better of the opening exchanges to take an early 6-0 lead.
Hook banged over a penalty from 45 metres out with barely two minutes on the clock and added a second from even further after Paul Burke was off target.
Yet Leicester are experts when it comes to winning finals and they silenced the huge travelling contingent of supporters from South Wales with four unanswered tries before half-time.
Tom Varndell went under the posts on 13 minutes after snatching Burke's kick out of Justin Marshall's clutches. Burke was again the provider just 60 seconds later when he spotted the mismatch between flanker Tom Croft and pint-sized Williams; Leicester's forward palmed the ball down to Danny Hipkiss whose return pass sent Croft galloping over for a second score.
Leicester's dominance was rewarded with the bounce of the ball as Ben Kay stormed over on 25 minutes before Alesana Tuilagi scored after a fortunate bounce opened the door for Harry Ellis to open a staggering 28-6 lead for the English giants.
Hook finally plugged the flow with a penalty before half-time to get the scoreboard moving again for the Ospreys - and sparked a remarkable comeback.
Lyn Jones's half-time talk blew the Ospreys into life as the Welsh region stunned Twickenham with three tries in 11 minutes. Byrne kicked off the fightback after Walker, Andrew Bishop and Williams combined to punish a poor Leicester clearance. Williams then added a second, finishing off a stunning counter-attack from deep inside their own half.
A huge defensive effort kept the Tigers at bay until Walker led the breakout and Byrne's long pass to Williams sent the wing scurrying from Leicester's grasp from a standing start. He struck again moments later to bring the Ospreys back to within a score.
Yet just as the Ospreys were building a head of steam, Varndell escaped to score on 62 minutes and a conversion and penalty from Andy Goode kept Leicester just out of reach.
Walker kept Osprey hopes alive until the whistle when he stretched out to score seven minutes from time but Guinness Premiership leaders Leicester shut up shop to ensure the EDF Energy Cup stays in England for another year.
Ospreys: Tries: S Williams (2), L Byrne, N Walker. Cons: J Hook (3). Pens: J Hook (3)
Leicester: Tries: T Varndell (2), T Croft, B Kay, A Tuilagi. Cons: P Burke (4), A Goode. Pens: A Goode (2)
Ospreys: Byrne, S. Williams, Parker, A. Bishop, Walker, Hook, Marshall, D. Jones, Bennett, A. Jones, Cockbain, A. Jones, R. Jones, Thomas, Tiatia
Replacements: Terblanche, Connor, Spice, B. Williams, James, Powell, Pugh
Leicester Tigers: Vesty, Varndell, Hipkiss, Gibson, A. Tuilagi, Burke, Ellis, Castrogiovanni, Chuter, White, Cullen, Kay, T. Croft, S. Jennings, M. Jennings
Replacements: Goode, F. Murphy, Moreno, L. Deacon