Nani set Portugal on their way with a left-foot drive and further goals from Simao Sabrosa, Miguel Veloso and Edinho saw them clinch second place in Group One with 19 points, two points adrift of winners Denmark but one point ahead of Sweden.
The result completed the first stage of a qualifying comeback for Portugal, who had looked down and out at one stage after winning just one of their first five games.
"I'm very satisfied as winning this match means going forward in this marathon, in a group that in the end was one of the tightest in the fight for the top two places," Portugal coach Carlos Queiroz said.
"I think it's fair to say that it will probably be the unseeded teams that are right now more worried," said Queiroz, expressing no preference on the opponents.
Just before half time, Simao secured the second goal. Deco's pass from midfield was deflected but still reached Simao, who curled it in.
Miguel Veloso added Portugal's third on 52 minutes with an easy tap-in from a Nani cross, and substitute Edinho completed the rout in the 90th minute by running on to a Simao through ball and rounding the keeper.
