Leicester began brightly, with the Ospreys not even reaching their 22 in the first 12 minutes, and the home side could feel hard done by to just have Flood's first penalty to show for their dominance.
Flood and Matt Smith in particular stretched the Welsh defence, but once they had endured the initial battering, the Ospreys went on the offensive, with Bowe and Hook showing dangerous touches.
Despite having the smaller pack, Leicester dominated the forward battle which seemed to rattle the visitors.
This was demonstrated when they conceded a penalty at the scrum which Flood kicked over from just inside his own half, and they compounded it by being caught off-side at the restart.
The Ospreys' problems could have grown even worse had Johnny Murphy not been called back for a forward pass when he was breaking clear on the left, and then he twice failed to find Smith with what would surely have been try-clinching passes.
Despite Leicester's dominance, they kicked only four penalties, and the Welsh team finally got on the scoreboard just before the break when a sustained period of pressure ended with Williams's drop-goal.
Paul James's charge-down of Harry Ellis's kick nearly gave the Ospreys a dream start to the second half, but Leicester got themselves out of a corner and stayed nine points clear until Hook's penalty, which came just after Flood limped off.
His replacement Derick Hougaard just missed with a drop-goal attempt but it looked like Leicester had done enough to hold on for the win, until Bowe's breakaway took the ball right down to the Tigers' line to set up a tense finale.
Geordan Murphy hauled him down just short of the line, but it took play up to a very threatening position for the Ospreys.
They launched a ferocious forward assault to try and snatch a late win, with Filo Tiatia driving them forward, but his error gifted possession to Leicester and allowed them to hoof the ball clear.
Leicester captain Martin Corry:
"It was a first-class performance by Toby Flood. There is an air of confidence about him, not arrogance, and he delivered.
"We are extremely happy to have Toby playing in a Leicester shirt.
"To beat a team of the Ospreys' calibre is very satisfying - these type of games are all about the result.
"Our endeavour in the first half was the best it has been this season."
Ospreys coach Sean Holley:
"We are very pleased with the losing bonus point. We are right in this pool, fighting.
"When you come to Welford Road, Leicester have got a 16th man - the crowd - and you expect an early onslaught.
"Teams coming here expect a tough game, and Leicester deserved their win, but I thought our players showed tremendous character."
Leicester: G. Murphy, J. Murphy, Hipkiss, Mauger, Smith, Flood, Ellis, Ayerza, Kayser, White, Corry, Kay, Croft, Woods, Crane. Replacements: Tuilagi for Smith (58), Hougaard for Flood (57), Chuter for Kayser (62), Cole for White (65), Blaze for Corry (74), Wentzel for Kay (69). Not Used: Dupuy.
Ospreys: Byrne, Walker, Bowe, A. Bishop, Williams, Hook, Wells, James, Hibbard, A. Jones, Wyn-Jones, Evans, Thomas, Holah, R. Jones. Replacements: Biggar for Walker (50), Webb for Wells (72), Bennett for Hibbard (44), Gough for Wyn-Jones (67), Tiatia for Thomas (50). Not Used: D. Jones, Smith.
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