In a game marred by a fight that saw two players sent off Vieri rounded off a fine move in the 14th minute to grab the winner.
It was on the counter-attack that Inter looked at their most potent and returning hero Hernan Crespo played a key part in the goal.
The Argentine got his head to an Emre cross and flicked into Vieri's path.
The Azzurri star is in deadly form this campaign and he made no mistake despatching only his second goal of the Champions League this year.
Francesco Toldo was forced to make a good save from David Albelda from range - the Italian international getting down well as the ball came through a crowd of players.
The second half saw the match degenerate into a battle of attrition, and things turned violent when Marco Materazzi went in hard on Ruben Baraja.
The ensuing melee saw several players get involved, and two - Albelda and the often belligerent Emre - dismissed for violent conduct.
Valencia threw everything forward in the desire for an away goal - but Inter clung on and will hope they can defend as well in the Spanish leg.
