Saviola smashed the ball into the roof of the net in a potentially-decisive finish to the match after PSV looked to have clawed their way back into contention with an 80th-minute goal from Zakaria Labyad.
Until Labyad gave PSV hope 10 minutes from time, Benfica largely dominated with Eduardo Salvio's two strikes either side of half-time adding to Pablo Aimar's opener seven minutes before the break.
Benfica should have been ahead after seven minutes when Saviola hit the post, and the same player came agonisingly close with a neat lob over PSV keeper Andreas Isaksson minutes later.
PSV came close when Balazs Dzsudzsak sent in a superb cross from the left flank and Marcus Berg got in above the static Benfica defence but could only head the ball wide with the goal at his mercy.
Aimar swept Benfica ahead when he struck a shot through Andreas Isaksson's legs and the home side added their second just before the break when Salvio scored after superb work from Fabio Coentrao.
It took only seven minutes of the second half for Salvio to grab his second, when he beat two men in the box before firing home. Oscar Cardozo came close as Benfica looked in good shape to move even further in front.
They looked set to pay for their failure to get a fourth when PSV finished strongly and grabbed their away goal when Labyad - who had only been on the pitch for 30 seconds, poked home after a Jeremain Lens effort was parried into his path.
But just when the second leg looked a distinctly healthier option for the Dutchmen they reckoned without Saviola whose brilliant finish leaves his side well in control going into the second leg.
Benfica 4-1 PSV: Match Report - view commentary, squad, and statictics of the game as it happened.