Porto, last season's UEFA Cup winners, scored a heart-stopping equaliser at the death to draw 1-1 at Old Trafford and beat Manchester United 3-2 on aggregate while Deportivo became the first Spanish side to beat Juventus at home for 42 years to win 1-0 on the night and 2-0 on aggregate.
Chelsea and Olympique Lyon also reached the last eight with first knockout round aggregate wins over VfB Stuttgart and Real Sociedad. Chelsea went through 1-0 on aggregate and Lyon 2-0.
The most dramatic moment of a night of only four goals came in the dying seconds at Old Trafford after Manchester United appeared to have done enough to squeeze into the last eight for the eighth successive year.
United took the lead against Porto with a 32nd minute Paul Scholes header which they held until the 90th minute.
That would have been enough to give them an away goals rule victory after losing the first leg 2-1 in Porto.
Scholes also had a close-range goal wrongly disallowed by a linesman's flag just before half-time which would have put United 2-0 ahead.
"That's proved vital, the referee or the linesman did not do his job properly," said disappointed United coach Alex Ferguson afterwards.
Porto, who had lost all six of their previous European matches in England, equalised in the 90th minute when a free-kick by Benni McCarthy, who scored both Porto goals in the first leg, was parried by American goalkeeper Tim Howard straight into the path of Portuguese international midfielder Costinha.
Porto coach Jose Mourinho ran from his seat in the stands and more than 50 metres to embrace his players while most of the 67,000-plus fans inside the stadium were stunned into disbelieving silence.
Mourinho was ecstatic afterwards: "To play like this and get a result here was fantastic, not just for Porto and our supporters but the whole of Portugal," he said.
Deportivo became the first Spanish side to beat Juventus at home since Real Madrid won there in a European Cup quarter-final in 1962, when Uruguayan international Walter Pandiani struck after 12 minutes to earn a 2-0 aggregate win which put them into the quarter-finals for the third time.
LONG CLEARANCE
Pandani scored with a half-volley after a long clearance from goalkeeper Jose Molina bounced between Juve defenders Paolo Montero and Ciro Ferrara.
Juve were hampered by the absence of injured French striker David Trezeguet, who missed the game, and Italian striker Alessandro Del Piero who limped off injured after seven minutes.
Deportivo's appearance in the last eight seemed an unlikely prospect last November when they lost 8-3 to Monaco in the first group phase while Juve's exit is just as surprising following their 7-0 thrashing of Olympiakos Piraeus in December.
"We are talking about two teams who have eliminated Juventus and Manchester United which should say something," Juve Marcello Lippi said of the night's big winners.
"They are both playing with real confidence and have real quality. You could call them the 'new force' if you choose but certainly they are two emerging sides at this level."
CHELSEA THROUGH
Chelsea, another emerging force thanks to the millions of Russian owner Roman Abramovich, went through after a match that produced few chances for either side. The tie was ultimately settled by the own goal conceded by Stuttgart's Portuguese defender Fernando Meira two weeks ago.
Lyon seemed to be going through the same way until Juninho Pernambucano doubled their lead after 77 minutes with a beautifully-crafted goal.
The four remaining first knockout round matches between Arsenal and Celta Vigo (3-2 after the first leg), holders AC Milan and Sparta Prague (0-0), Real Madrid and Bayern Munich (1-1) and AS Monaco and Lokomotiv Moscow (1-2) will be played on Wednesday.
The draw for the quarter-finals will take place in Nyon on Friday.
