Valdes, a Panamanian, was fed by teammate Jose Herrera of Panama deep inside Juventus' penalty area. Valdes kicked the ball into the net from 10 meters in the 60th minute.
Forward Luis Oliveira of Brazil missed two clear chances to score for the home team in the last 10 minutes of play at Sant'elia Stadium.
Juventus, the defending UEFA Cup champion, produced few scoring opportunities because its best player, Roberto Baggio, was well covered by Cagliari defenders.
The second-leg match will be played in Turin on March 15.
In the other UEFA Cup quarterfinal played Tuesday, Dutch international Wim Jonk scored twice in the first half to lead Internazionale of Italy to a 3-1 victory over Germany's Borussia Dortmund in the away leg.
Jonk opened the scoring in the 33rd minute and took advantage of a mistake in Dortmund's defense to score again three minutes later as the capacity 35,800 crowd booed and whistled their side.
Michael Schulz raised Dortmund's hopes of salvaging a draw by reducing the deficit in the 83rd minute.
But last year's beaten finalists were left with a mountain to climb in the second leg when Russian international Igor Shalimov scored the Italians' third two minutes from time.
The result marked Dortmund's second straight 3-1 home defeat to an Italian side following last season's UEFA Cup finals, where Juventus won 6-1 on aggregate to claim the European trophy.
In Portugal on Tuesday night, a last-minute goal gave Benfica a lucky 1-1 draw against Munich's Bayer Leverkusen in a first leg match of the Cup Winners Cup quarterfinals.
Both teams started off on equal footing, with the fiesty Benfica offense shut down. But Bayer Leverkusen finally broke through in the 66th minute with a head-in goal from backfielder Markus Happe after a corner kick.
That looked like the end for bad luck-plagued Benfica, but striker Isaias Soares blasted the 90th minute equalizer to bring the Lisbon draw.
Some 85,000 fans turned up on a chilly, windblown night to watch the game at Lisbon's Benfica's Luz Stadium.
The second leg of the Cup Winners Cup quarterfinals is scheduled for Tuesday, March 15, in Munich.
(AP, UPI, Reuters)
A Message from The Moscow Times:
Dear readers,
We are facing unprecedented challenges. Russia's Prosecutor General's Office has designated The Moscow Times as an "undesirable" organization, criminalizing our work and putting our staff at risk of prosecution. This follows our earlier unjust labeling as a "foreign agent."
These actions are direct attempts to silence independent journalism in Russia. The authorities claim our work "discredits the decisions of the Russian leadership." We see things differently: we strive to provide accurate, unbiased reporting on Russia.
We, the journalists of The Moscow Times, refuse to be silenced. But to continue our work, we need your help.
Your support, no matter how small, makes a world of difference. If you can, please support us monthly starting from just $2. It's quick to set up, and every contribution makes a significant impact.
By supporting The Moscow Times, you're defending open, independent journalism in the face of repression. Thank you for standing with us.
Remind me later.