The Bhoys are still second in Group F behind leaders Manchester United but Gordon Strachan's side were a shadow of the team that beat their Portuguese opponents by the same scoreline at Celtic Park two weeks ago.
The runaway SPL leaders never recovered from a nightmare start that saw Gary Caldwell score an own goal in the tenth minute before the Scotland international's error allowed Nuno Gomes to double Benfica's lead 12 minutes later. Substitute Andrei Kariaka completed the scoring in the closing stages.
Fabrizio Miccoli had already gone close to opening the scoring when the unfortunate Caldwell turned Nelson's deep cross past his own keeper Artur Boruc.
Caldwell then misjudged Quim's hopeful long pass and, when he deflected the ball to Nuno Gomes, the Benfica star lashed his shot past Boruc.
Celtic tried to hit back and Stephen Pearson fired wide before the interval but that was a rare foray forward by the outclassed visitors.
Benfica dominated the second half and always looked likely to add to their tally. Miccoli's close-range drive was blocked before, with 14 minutes left, Kariaka turned Nelson's low cross home.
Nuno Gomes almost added a fourth goal for the hosts before the final whistle as Benfica moved to within two points of Strachan's side with two group games to play.