The two teams have already met in the pool stages of the competition this season Stade won that encounter 26-15 but this victory will be by far the sweeter given what was at stake: a place in the quarter-finals.
And the French champions richly deserved to progress in the tournament as they competed on equal terms in the first half before assuming full control after the break with Leicester running out of steam, especially up front.
Dominguez, 38 in April, proved the difference after booting 16 points without missing a single shot at goal and matching his sublime kicking performance with some inventive play at fly-half which he capped with an injury-time try.
In contrast, Leicester tried out four different kickers who failed to hit the target once in six attempts between them a shocking return that resulted in the Tigers failing to reach the Heineken Cup last eight for only the second time in their history.
Dean Richards' men showed promise with tries from Harry Ellis and Ollie Smith while number eight Henry Tuilagi caused Stade all sorts of problems with his powerful running, but they never showed up for the second half.
It was a sorry way for Neil Back to mark his 300th Leicester appearance and Dorian West his 200th.
Scorers for Leicester: Tries: Ellis, Smith. Pens: van der Westhuyzen.
Stade Francais: Tries: Auradou, Dominguez. Cons: Dominguez 2. Pens: Dominguez 4.
LEICESTER: Booth, Smith, Gelderbloom, Lloyd, F. Tuilagi, van der Westhuyzen, Ellis, Rowntree, West, Morris, M. Johnson, Kay, W. Johnson, Back, H. Tuilagi, Myring. Replacements: Myring for Booth (20), Corry for F. Tuilagi (67), Pez for Myring (67).
STADE FRANCAIS: Corleto, Henandez, Glas, Liebenberg, Dominici, Dominguez, Pichot, Marconnet, Blin, De Villiers, Auradou, Marchois, Moni, Tabacco, Rabadan.
Replacements: Jechoux for Moni (70).
Referee: Alain Rolland (Ireland).