Three tries in the final eight minutes from Toby Flood, Ben Youngs and Manu Tuilagi added to Tuilagi's first half score to give the Tigers a much-needed bonus point from the must-win encounter.
Flood added a further 19 points with the boot in a superb kicking display, while Ospreys' points came through Ryan Jones' second-minute try plus 17 points from fly-half Dan Biggar.
Ospreys grabbed the lead in the second minute when Ryan Jones drove over from close range and Biggar converted to put his side 7-0 up.
Ten minutes later the fly-half extended the Welsh side's advantage with a fine long-range penalty from the halfway before Toby Flood finally booted Leicester onto the scoreboard in the 28th minute.
Leicester levelled the scores three minutes later when some superb link play from the Tigers backs put Tuilagi in on the right for a beautifully worked try and Flood converted.
Biggar put his side back in front almost immediately after the break but Flood put the Tigers in front for the first time with two penalties and then extended the lead on 49 minutes with a 47 metre effort.
Biggar hit back with two of his own to put his side back on level terms going into the final quarter before Flood wrested back the lead with a superb 53 metre kick with 14 minutes to go.
Moments later the England fly-half opened the flood gates with a brilliant interception to all but guarantee the win and Youngs and Tuilagi followed in quick succession to seal the bonus point.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.