It was recent signing Sotirios Kyrgiakos who headed home the winner for the home team with just six minutes to go.
Twice Rangers had taken the lead, first through Peter Lovenkrands and then Dado Prso, but on each occasion Kepler Pepe drew the Portuguese side level.
The result probably flattered Rangers, especially as the visitors enjoyed the lion's share of the possession and chances.
After a bad miss by Miguel Ricardo Costa and after Jorginho's shot ended on top of the net, the home side took the lead from almost their first attack in 35 minutes.
Fernando Ricksen's long ball was left by Hamed Namouchi and Lovenkrands was first to react, prodding the ball past Vitor Baia.
Francis Jeffers required too many touches when two chances fell to him just before half-time.
Porto equalised shortly after the break when Pepe headed powerfully home from an Alan corner.
Rangers restored their lead on the hour mark when Barry Ferguson's free-kick was flicked back across goal by Kyrgiakos, with Prso getting a touch to force the ball home with the Porto keeper looking suspiciously at fault.
Once again Pepe forced the ball home from a corner with the Rangers defence all at sea.
Incredibly Rangers took the lead when Ferguson collected a short free-kick before chipping a pass down the middle which Kyrgiakos headed home via the post.