The game was ever so close for 70 minutes with each teams taking the lead a few times until it opened up to see Toby Flood, Ben Youngs and Manu Tuilagi all go over and secure the goods for the Tigers.
Following their poor display in Toulouse last week, Leicester knew they had to win to have any realistic chances of qualifying for the knock-out stages and put on a much better performance back at their beloved Welford Road.
They attacked the gain lined with Youngs and Flood in superb form from half-backs as well as showing much more urgency to play on the front foot and put the pressure on the Ospreys.
The Welsh side were dominated in the set pieces but showed great character to always stay within striking range.
Their defence was superb for 70 minutes and Dan Biggar was perfect with the boot to capitalise on any given opportunity.
However, poor discipline and tactical errors in the last ten minutes means they leave Welford Road without any points to show for their efforts and now prepare to face Toulouse back to back as they still remain on course for the qualification.
The Welsh enjoyed a perfect start when former captain Ryan Jones barged his way over for the opening try of the game after only two minutes.
Biggar added the extras and and a penalty soon after to put the Ospreys 10-0 in front after 12 minutes.
Leicester got themselves right back in the game by building up the pressure but handling errors prevented them from scoring until Flood kicked a penalty on the half-hour mark.
The pressure eventually proved too much for the Ospreys and Manu Tuilagi went over for a classic Tigers’ try.
Flood attacked the line to find Niki Goneva inside and two offloads later the crowd went off their seat.
The fly-half added the extras and the score was leveled at 10-10 at the break.
Biggar put the Ospreys back in front with an early second-half penalty but three penalties from Flood saw Leicester take the lead for the time of the game as they seemed to control the game more and more.
But the Welsh fly-half leveled the score once again with two penalties in quick succession to set up a thriller with 20 minutes to go.
Flood put the home side three points clear with a superb penalty from 57 metres before the England fly-half intercepted a ball from that same spot and raced over to take a vital 29-19 lead after his own conversion.
The flood gates opened up and all a sudden the Tigers were chasing a bonus-point that never seemed reachable for most of the game.
Youngs went over before Tuialgi rounded a superb performance from the home side on the last play of the game.
For Leicester
Tries: Tuilagi 2, Flood, Youngs
Conversions: Flood 2
Penalties: Flood 5
For Ospreys
Try: R. Jones
Conversion: Biggar
Penalties: Biggar 5
Sin bin: Bevington
Leicester: Hamilton; Morris, Tuilagi, Allen, Goneva; Flood, Youngs; Mulipola, Youngs, Cole; Kitchener, Parling; Mafi, Waldrom, Crane (capt.).
Replacements: Chuter, Ayerza, Castrogiovanni, Deacon, Thorpe, Harrison, Ford, Smith.
Ospreys: Fussell; Dirksen, Bishop, Beck, Walker; Biggar, Fotuali’I; Bevington, Hibbard, A. Jones; Wyn-Jones (capt.), Evans; R. Jones, Tipuric, Thomas.
Replacements: Dwyer, D. Jones, Jarvis, Stowers, Bearman, Webb, Morgan, Isaacs.
Referee: Romain Poite (France)
Star man: Toby Flood – Leicester
NICK VERDIER