Heorhiy Sudakov opened the scoring at the end of the first half for the visitors, with Vangelis Pavlidis netting the second from the penalty spot before the hour mark.
Franjo Ivanovic rounded off the rout for Benfica, who moved second in the table, five points behind leaders Porto, having played one fewer match.
The veteran Portuguese coach, back at the helm of the Eagles 25 years on, celebrated the third goal furiously, pumping his fist and kicking a cone.
The 62-year-old, who also coached Porto in the Portuguese top flight before leaving in 2004 to join Chelsea, will face both those teams within the next 15 days.
Mourinho, who won trophies with Real Madrid, Manchester United, Inter Milan as well as coaching various other sides, was sacked by Fenerbahce in August.
Benfica ousted coach Bruno Lage this week after a surprise defeat in the Champions League by Azerbaijani minnows Qarabag and appointed Mourinho as his replacement on Thursday.
His first spell at the club lasted just 11 games, but Mourinho said on his presentation that he was more "mature" and "altruistic" now.