Porto, European champions in 1987 and UEFA Cup winners last season, were in control for almost the entire game but a hard-working Deportivo side kept them at bay.
With the game drifting towards a goalless draw, Deportivo had Jorge Andrade sent off three minutes from time for a needless kick on Deco Souza.
The Portuguese centre-back will miss the second leg and his absence, along with that of booked midfielder Mauro Silva, will be a threat to Depor's hopes of reaching a first European final.
"The referee was very rigorous as Jorge was really just having a joke by kicking out at an old friend but it's up to him to make those judgements," Mauro Silva told Spanish television.
"It's a real shame that both me and him will miss the next game but you can't control those sort of things in the heat of the moment."
Tuesday's semi-final saw a more decisive result with Monaco taking a big step towards the final in Gelsenkirchen, Germany on May 26 with a 3-1 victory at home to Chelsea.
SUBLIME CHIP
Porto's coveted midfielder Maniche Ribeiro hit the bar with a sublime chip from 25 metres after an hour in what was without question the best moment of the second semi-final, played at the Portuguese side's beautiful new Dragao stadium.
There was another close call for Deportivo when their defender Noureddine Naybet almost provided an own goal and Porto substitute Edgaras Jankauskas should then have scored with a header from a dangerous free kick by Deco Souza late on.
Deportivo had only one opportunity to claim an away goal that would have put them in control of the tie, Walter Pandiani volleying wide from inside the penalty area after being left unmarked in the ninth minute.
La Coruna is just 275 kms from Porto across the border and the game had the feel of a local derby throughout.
To reach the semi-finals, Deportivo had needed a heroic 4-0 win in the second leg of their quarter-final against AC Milan after a 4-1 defeat in the away game and their objective in Porto was clearly to avoid a similar result.
A series of biting challenges from the Spaniards set the scene in the opening half-hour and Porto were unable to make any headway with their passing, despite the best efforts of Carlos Alberto and Deco.
GREAT CONTROL
Deportivo might have gone ahead in the ninth minute, when Manuel Pablo's sweeping cross from the right picked out Pandiani in space in the area.
After showing great control to bring the ball down, the Uruguayan striker had an age to place his shot but only succeeded in volleying high and wide.
Porto did not manage a shot until the 15th minute, when Deco blazed over from outside the box after a free kick on the right had been played short.
There was then little of note from either side before Naybet came desperately close to giving Porto the lead with an own-goal.
Deco managed to squeeze a pass through to Carlos Alberto on the left of the area and his cross flashed wide after striking Naybet's heel.
Deportivo occasionally looked menacing on the break but Victor and Albert Luque were both guilty of poor crosses.
Porto coach Jose Mourinho brought on Jankauskas at halftime and the big striker almost scored eight minutes from time when a darting run gave him a free header that went a fraction wide.
Before that, Maniche had come agonisingly close to a goal with his well struck chip but Porto were otherwise lacking in inspiration and Andrade's sending-off came too late to give them any real advantage -- at least in the first leg.
