Billy Twelvetrees scored Leicester's second try and also kicked nine points
Leicester fought back from 26-8 down with a late Jeremy Staunton try to deny Ospreys victory in a pulsating Heineken Cup pool encounter at Welford Road.
The Tigers led 8-0 early on but Ospreys responded with 26 points in 20 minutes.
Fly-half Dan Biggar landed three penalties and converted tries from Shane Williams and Tommy Bowe.
Tigers replied with tries from Billy Twelvetrees and Lucas Amorosino but two more Biggar penalties put Ospreys 32-22 ahead before the hosts' rousing finish.
They might even have won it late on but, severely depleted by injury, will probably settle for a three-point haul ahead of a bonus-point mission in Italy against Viadana next weekend.
The Ospreys, though, will return to Swansea to prepare for the visit of Clermont Auvergne reflecting on a missed opportunity to make a real statement about their European ambitions.
I think it is a missed opportunity for us
Ospreys captain Ryan Jones
Having established a commanding lead, they allowed their hostsback into the game before half-time and then failed to close out a 10-point lead in the final quarter.
With the likes of Geordan Murphy, Alesana Tuilagi, Toby Flood and Sam Vesty already on the injured list, Leicester were forced into making four late changes to their backline before kick-off.
England internationals Harry Ellis (knee) and Dan Hipkiss (flu), former All Black Aaron Mauger (groin) and wing Matt Smith (hamstring) all failed fitness tests.
But the Tigers roared out of the blocks and had the opening try on the board inside two minutes.
From quick line-out ball, fly-half Jeremy Staunton sent Anthony Allen - one of those who had come into the side - skating through Biggar's attempted tackle.
The centre shipped the ball onto Scott Hamilton who sent Johne Murphy powering through the cover to touch down in the right corner.
Staunton missed the conversion, but landed a simple penalty in the 10th minute to stretch the lead to 8-0.
The Ospreys, thrashed by Munster in last season's quarter-finals, might have feared the worst at that stage, but they transformed the match with a barrage of points.
Biggar banged over a long-range penalty, after Julian White was pinged at a scrummage, but the veteran England tight-head was quick to show his power to earn the Tigers a penalty, only for Staunton to lose his bearings with the kick.
Shane Williams slides in to score the Ospreys' opening try
But suddenly James Hook started to find space to spark the visitors' backline, only for the first move to break down with Bowe's ambitious pass to Nikki Walker.
But Biggar's second penalty made it 8-6 and a minute later, Hook and Biggar combined to great effect, the latter cutting a superb angle onto Hook's inside pass before sending Williams in for a simple finish, Biggar converting for a 13-8 lead.
The young fly-half provided a further illustration of his growing confidence by calmly slotting a drop-goal to extend the advantage.
The Ospreys' then enjoyed another bonus when a poor pass from Staunton drifted behind its target and Bowe greedily gobbled up the loose ball to sprint away for the visitors' second try.
Biggar again added the extras, and when he landed another penalty after 34 minutes, Ospreys were in command at 26-8 up.
But Tigers hit back immediately after Lee Byrne dropped a high ball, Allen's flipped pass sending Twelvetrees, a last-minute replacement for the ill Hipkiss, in for the try.
Ospreys scrum-half Mike Phillips was penalised for barging his knee into the centre's back in the act of scoring.
Twelvetrees, taking over the kicking duties, picked himself up to land the conversion, and with the game resuming with a penalty, saw his kick from halfway come back off the right upright.
He was then off target with another long-range effort to leave the Tigers trailing 26-15 after a frenetic first half.
If the Ospreys were un-nerved by seeing their lead eroded, they enjoyed an early boost on the resumption as Biggar slotted another penalty to give them a 14-point cushion.
But the hosts swiftly reduced that to seven with a second try from first-phase possession, Hamilton scooting round Phillips' attempted tackle before releasing Amorosino for the left corner.
Biggar and Twelvetrees exchanged further penalties to leave the Ospreys holding a seven-point lead for the last 13 minutes.
Leicester laid siege to the Welsh region's line and were rewarded when Staunton barrelled over in the 76th minute, Twelvetrees converting to ensure a breathless encounter ended honours even.
Leicester head coach Richard Cockerill:
"We had players unavailable and pulling out at the last minute but the attitude to just go out and play and not give up is what this side is about.
"The spirit of the players was fantastic. I knew we would take the game to them and we could have won it at the end. I thought we out-played them for large parts of the game.
"We pride ourselves on having people who want to play for us and not for the money. You can buy a team but you can't buy spirit."
Ospreys director of rugby Scott Johnson:
"If you had offered us two points prior to coming here we'd have taken it but we are totally disappointed.
"We controlled the scoreboard for large parts of the game but it came down to the fact we couldn't get quality ball to play off often enough. Without quick ball you can't play football."
Leicester: Hamilton; J Murphy, Allen, Twelvetrees, Amorosino; Staunton, Grindal; Ayerza, Chuter, White, L Deacon, Kay, Croft, Moody, Crane. Replacements: Newby for Allen (40), Castrogiovanni for White (47), Parling for Kay (52), B Youngs for Grindal (66), Stankovich for Ayerza (78). Not Used: Duffy, T Youngs, B Deacon.
Ospreys: Byrne; Walker, Bowe, Hook, Williams; Biggar, Phillips; James, Bennett, Griffiths, A-W Jones, Thomas, Collins, Holah, R Jones. Replacements: Bishop for Byrne (51), Hibbard for Bennett (61), Gough for Thomas (61), Tiatia for Collins (74). Not Used: Mitchell, Bevington, Nutbrown, Parker.
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