Celtic had twice come from behind with headers by Henrik Larsson, the Swedish striker's 200th and 201st goals for the Scottish club, to leave the final level at 2-2 at the end of 90 minutes.
The deadlock set up the prospect of the final being decided on the new silver goal rule, when the side leading at the end of either period of extra time is deemed the winner.
There were no further goals in the first 15-minute spell, despite the fact that Celtic had defender Bobo Balde sent off just five minutes in.
Porto eventually made their numerical advantage tell, however, after Derlei, who had scored his side's opener in first-half stoppage time, gathered a loose ball and beat Robert Douglas with a thumping shot.
Celtic pressed forward for the remaining five minutes, plus four agonising minutes of stoppage time, but there was to be no heroic third equaliser even after Porto's Nuno Valente was sent off to even up the numbers.
Substitute Shaun Maloney blasted the resulting free kick well over the bar and Porto held on for their first major continental title since their European Cup win over Bayern Munich in 1987.
They are also the first Portuguese club to win the UEFA Cup.
Celtic manager Martin O'Neill must now lift his players for their final Scottish premier league game of the season on Sunday, when the title is at stake.
He told BBC television: "I think we've done Scottish football
Celtic, European champions in 1967, were appearing in their first continental final since 1970 and both sides started nervously.
Portuguese champions Porto gradually took control in the first half through the guile of Deco and they were rewarded when Douglas managed to push away Dmitri Alenitchev's volley only for Derlei to tuck in on the rebound.
Celtic needed a response early in the second half to unsettle Porto and it arrived within two minutes of the restart.
Didier Agathe arrowed in a cross to the far post where Larsson headed back across Vitor Baia and in off a post.
The equaliser brought roars from a Celtic crowd outnumbering Porto supporters by around three to one but the Portuguese contingent were singing again in the 54th minute when Alenitchev restored their lead.
The Russian was played into space by Deco's neat ball and he beat Douglas with a cool finish from around the edge of the area.
Once again, Porto had little time to celebrate as Larsson powered a header past Baia direct from a corner.
There were few chances for either side before a dramatic finale when Alenitchev intercepted a dreadful pass from Jackie McNamara and with the last kick of normal time flashed a shot just over.
Celtic chances of victory took a blow early in extra-time when Baldo was sent off for his second yellow card.
But the Scottish side still had chances before Derlei's dramatic late intervention settled the game as he grabbed his 12th and most decisive goal of this season's competition.