Not even the first appearance of the season from Wales centre Gavin Henson could inspire Ospreys to victory.
It now means they will have to win their remaining three matches to have any hope of reaching the last 16.
Within minutes of the start Henson waltzed through the Leicester midfield and looked certain to score before cutting inside where he was snapped up by Lions colleague Ollie Smith.
Former Wales prop Darren Morris then began a period of Leicester pressure which eventually resulted in fly-half Andy Goode opening the scoring with a penalty on 21 minutes.
That lead was short-lived. Ospreys scrum-half Jason Spice moved the ball from a ruck and Henson put fellow centre Sonny Parker in for the opening try of the game. Shaun Connor added the conversion and the Tigers seemed rattled.
However, Leicester quickly forced another penalty which Goode struck home from 30 yards.
Ospreys scored their second try from full-back Adrian Cashmore after Connor had split the Tigers’ defence. Connor missed the conversion but the Welshmen still led 12-6 at the break.
Leicester came out with all guns blazing in the second half, flanker Brett Deacon eventually overcoming brave resistance from Ospreys on their own line.
Goode missed the conversion but Leicester went in front when captain Martin Corry broke clear and set up Harry Ellis to score.
This time Goode converted and his then cross-kick was collected by hooker George Chuter to fall over the line from a third home try.
Goode’s conversion put his side 13 points ahead.
And as the game entered injury-time Austin Healey went over for the decisive fourth try to secure the bonus point.
: Vesty, Lloyd, Smith, Cornwell, Murphy, Goode, Ellis, Moreno, Chuter, Morris, L. Deacon, Kay, B. Deacon, Jennings, Corry.
: Buckland, Holford, Cullen, Abraham, Healey, Broadfoot, Hipkiss.
: Cashmore, Terblanche, Parker, Henson, Mustoe, Connor, Spice, D. Jones, B. Williams, A. Jones, Newman, Evans, Bater, Tandy, Thomas.
: Joel Jutge (France).