Both teams were forced to play for over half an hour with 10 men after Valencia's David Albelda and Inter's Belozoglu Emre were sent off after an ugly clash.
The Spaniards, who had been quiet up until the incident, piled on the pressure in the latter stages as they searched, in vain, for an equaliser and a vital away goal.
Inter take a slender advantage with them into the second leg in Spain in a fortnight but Valencia, runners-up in the Champions League in 2000 and 2001, will certainly feel they are capable of turning the tie around.
It was no coincidence that Valencia enjoyed so much possession in the final half hour as the red cards had robbed Inter of their most influential figure in the little Turk Emre.
The former Galatasaray schemer set up a chance for Vieri in the 11th minute, which the burly striker blasted straight at Valencia keeper Santiago Canizares.
A little later, running on to a pass from Francesco Coco, Emre broke to the byline and Hernan Crespo flicked his cross into the path of Vieri, whose diving header flew past Canizares.
Valencia might have equalised in the 38th minute when Albelda's low shot forced Inter keeper Francesco Toldo into a full stretch save - a warning
What had been a surprisingly low key game turned nasty though in the 57th minute when in an off-the-ball incident Albelda kicked Emre and the Turk reacted angrily, confronting the Spaniard and attempting to headbutt him.
After a scuffle involving at least 10 players, German referee Markus Merk dismissed the pair.
The San Siro crowd rained plastic bottles and fruits down from the stands towards Albelda as he headed for the tunnel but thankfully the mood on the pitch was calmer.
Francisco Rafete fired a shot just wide of Toldo's post and then Pablo Aimar jinked into the penalty area before firing in a low shot that the Inter keeper did well to save at his near post.
Inter coach Hector Cuper had made a surprising team selection leaving out Italy defender Fabio Cannavaro and Uruguayan striker Alvaro Recoba, bringing back centre half Marco Materazzi and Crespo, who were both returning from injury layoffs.
But Cannavaro was called on seven minutes from the end, replacing a tired Crespo and adding an extra man to an under-pressure defence as Inter clung to their lead.
There was more controversy at the end when Aimar went down inside the area under a challenge from Okan Buruk but Merk ruled that the Argentine had dived and instead of a penalty the Valencia forward got a yellow card.
