The star-studded Welsh outfit, who travelled to the east midlands without their suspended centre Gavin Henson, delivered a lacklustre display.
Ospreys wing wizard Shane Williams hardly received a pass, such was Leicester's dominance and control of possession.
Williams' scoring contribution was confined to a drop-goal, with James Hook adding a penalty - he also missed two shots at goal - as Tigers avenged their Twickenham defeat in last season's EDF Energy Cup final.
With a potentially try-laden trip ahead of them to Treviso next Saturday, Leicester are up and running in pursuit of a third Heineken Cup triumph that would match French giants Toulouse.
The Ospreys though must beat Liberty Stadium visitors Perpignan in six days' time, or risk a possible pool stage exit.
They will be relieved to have collected a losing bonus point, which could ultimately prove crucial in the quarter-final shake-up, but it was not a performance to frighten established European forces such as Toulouse, Munster or Wasps.
England wing Tom Varndell failed to make a Leicester starting line-up captained from the second row by Martin Corry, while summer signings Flood and Ben Woods both made their Tigers European debuts.
All the pre-match attention had been on Ospreys though, following their decision to ban Henson for two games.
Henson, who will also miss the appointment with Perpignan, was replaced by Andrew Bishop, while former Ulster wing Tommy Bowe lined up alongside him in midfield.
Wales coach Warren Gatland, who announces his squad for the autumn Tests on Tuesday week, was among a capacity crowd of 17,498, but the Ospreys gave him little to cheer.
The Leicester forwards showed an immediate appetite for battle, led by their uncompromising tighthead prop Julian White.
White set the tone, playing the game in Ospreys' collective face, and they could not cope.
Tigers were hungrier and quicker at the critical breakdown area, and it took Ospreys 14 minutes to break into Leicester's 22, by which time they were 3-0 behind.
Flood completed his penalty hat-trick early in the second quarter, landing one kick from a metre inside Leicester's half, but Tigers also blew three clear try-scoring chances.
Wing John Murphy sliced open the Ospreys defence, only for his pass to fly over full-back Geordan Murphy's head, then they repeated their double act before the ball drifted into touch.
Flanker Tom Croft galloped over the Ospreys line as half-time approached, only for referee Alain Rolland to call play back for a lineout after Tigers wing Matt Smith put his foot in touch during the build-up.
Flood's fourth successful penalty put Leicester 12 points clear, and it took the Ospreys 39 minutes to open their account through a Williams drop-goal.
Williams' left-footed strike went over via the post, and Rolland required confirmation from the video official before awarding it.
The Ospreys were relieved to troop off only nine points adrift, such had been Leicester's dominance, and a Hook penalty after 58 minutes further cut the deficit.
Hook, now operating at inside centre after the Ospreys sent on their Wales Under-20 fly-half Daniel Biggar, had earlier seen a long-range strike drift narrowly wide as Leicester came under sustained pressure for the first time.
A raft of Ospreys substitutions, notably the arrivals of flanker Filo Tiatia and prop Duncan Jones, generated much-needed momentum, while Leicester lost a limping Flood, who was replaced by South African Derick Hougaard.
The Ospreys went for broke as the clock ticked down, Bowe only narrowly being denied a breakaway try by Geordan Murphy's superb defensive work, but the Welsh side still secured an attacking scrum.
Leicester did not panic though, tackling feverishly before Hougaard took the pressure off with a decisive 50-metre clearance kick.