Rossi brace sees Villarreal through
The Spanish side must have been beginning to wonder where a goal was going to come from as Stefan Wessels saved everything that came his way until five minutes into the second half, when Rossi stabbed home a low Nilmar cross.
That goal cancelled out Hans-Henrik Andreasen's strike which had given Odense the narrowest of first-leg leads, and was the least Villarreal deserved for their domination of the tie.
The spectators at the El Madrigal were on their feet again midway through the second half when a wonderful cross from deep on the right flank from Cani was met by Rossi, leaving Wessels with no chance.
Odense knew that an away goal would still swing the tie back in their favour, but their hopes were dealt a huge blow when Bashkim Kadrii was sent off for a second bookable offence.
Numerical parity was restored when Borja Valero was shown a red card for a retaliatory headbutt on Andreas Johansson, but Villarreal put the outcome beyond doubt when substitute Carlos Marchena's shot was fumbled over the line by Wessels.
That sealed victory for Juan Carlos Garrido's side, who join Barcelona, Real Madrid and Valencia as Spain's representatives in Friday's draw for the group stages.
Last season's Danish league runners-up Odense had fought to win 1-0 on home soil just six days ago, but they never troubled Villarreal goalkeeper Diego Lopez, and it always seemed only a matter of time before the hosts found a breakthrough.
Playing with just three recognised defenders, and with summer signing Javier Camunas making his debut on the right wing, Villarreal went for the jugular straight away. Rossi saw an early effort sneak wide of Wessels' left-hand upright, while Valero saw another strike turned around the post.
Former Bayern Munich and Everton keeper Wessels then produced a fine double save to deny Camunas and Rossi as half-time approached, and Camunas turned and cracked another strike off the bar moments after the restart.
However, Rossi's brace and Marchena's late counter ensured that the Yellow Submarine return to the group stage for a third time, while Odense have the consolation of a place in the UEFA Europa League group stage.