Liverpool turned in a superb performance to beat Real Madrid 4-0 at Anfield, while Chelsea overcame Juventus following a 2-2 draw in Italy to book their place in the quarter-finals of the UEFA Champions League.
The Reds completely dominated the second leg of their tie against Juande Ramos' side and eased into the next round thanks to an early Fernando Torres strike, a Steven Gerrard brace and a late Andrea Dossena goal.
It was a more nervous night for Chelsea as they twice came from behind to hold Juve, with Michael Essien and Didier Drogba on target, and secure a 3-2 win on aggregate.
Elsewhere in Europe, Bayern Munich completed an amazing 12-1 aggregate victory over Sporting, while Villarreal saw off Panathinaikos 2-1 in a much more competitive tie.
The onus was on Real Madrid to attack at Anfield after losing the first leg 1-0 but it was Liverpool who came flying out of the blocks and Iker Casillas had to be at his best to deny first Torres, back in the starting XI following injury, and then Javier Mascherano.
Real were not able to withstand the onslaught for long and fell behind in the 16th minute, although there was a hint of controversy about the goal as Pepe slipped after a slight tug by Torres and Dirk Kuyt crossed for the Spaniard to tap the ball home.
Real had few complaints but they were left incensed by the decision to award Liverpool a penalty 12 minutes later when Alvaro Arbeloa headed the ball against Gabriel Heinze's shoulder. The referee ruled that Heinze had used his arm and Gerrard stepped up to send Casillas the wrong way.
Now 3-0 in front on aggregate, Liverpool were oozing confidence and they scored another goal two minutes into the second half as Ryan Babel broke down the left and crossed for Gerrard to smash the ball in on the half-volley.
Liverpool coasted through to full-time and substitute Dossena added late gloss to the scoreline from Mascherano's assist, to inflict on Real their biggest ever Champions League defeat.
Liverpool will be joined in the last eight by Chelsea, although their Premier League rivals were involved in a fierce scrap in Turin.
Juventus broke the deadlock with a fine goal on 19 minutes, Vincenzo Iaquinta slotting a low shot across Petr Cech after being released by a clever pass from strike partner David Trezeguet.
Didier Drogba appealed for an equaliser when his firm free-kick was gathered by Gianluigi Buffon, with replays suggesting the ball may just have crossed the goal-line.
The referee waved play on but Chelsea's disappointment was only temporary as Michael Essien, restored to the starting XI after months out with a serious knee injury, netted on the stroke of half-time after Buffon had pushed Frank Lampard's excellent volley onto the crossbar.
Juventus now had to win by two clear goals to progress to the last eight and they pushed Chelsea back in the second half, but Cech was on top form to keep out Trezeguet's header.
Juventus' hopes appeared to suffer a critical blow when Giorgio Chiellini was sent off for dissent 20 minutes from time, but Chelsea then conceded a penalty for a Juliano Belletti handball and Alessandro Del Piero coolly converted from 12 yards.
Belletti made amends with seven minutes remaining as he supplied the cross for Drogba to tap home and finally settle Chelsea's nerves.
Bayern Munich smashed seven past Sporting to underline their credentials as possible dark horses.
Sporting needed to score an early goal to have any chance of overturning their 5-0 deficit but Bayern were not in the mood to be generous and extended their aggregate lead after seven minutes as Lukas Podolski's powerful left-footed effort from outside the area flew into the top corner.
The Portuguese side then proceeded to capitulate to an embarrassing extent as comical defending allowed Bayern to run riot.
A horrendous mix-up between goalkeeper Rui Patricio and Anderson Polga presented Podolski the opportunity to score with an overhead kick in the 34th minute, and Anderson Polga's night went from bad to worse five minutes later as he sliced an extravagant attempted clearance into his own net from a corner.
Joao Moutinho reduced Sporting's arrears with a spectacular strike in the 42nd minute but there was still time for Bastian Schweinsteiger to turn home Christian Lell's cut-back before half-time and make it 4-1 on the night.
Mark van Bommel made it 5-0 in the 72nd minute after good work from Thomas Muller but the misery was not yet over for Sporting.
Miroslav Klose got in on the act with nine minutes to go and Muller took advantage of more poor defending to clinch a 7-1 win on the night and a record-breaking aggregate success
In Greece, Villarreal beat Panathinaikos 2-1 to seal a 3-2 triumph over the two legs.
The tie was delicately poised following a 1-1 draw in Spain a fortnight ago and there was little to choose between the sides in the first half of the second leg, although Villarreal's Ariel Ibagaza had a goal disallowed.
Ibagaza was not to be denied as the second period got underway, however, with the Argentine playmaker providing the finishing touch to a flowing move as he scored from the edge of the box.
Vangelis Mantzios drew Panathinaikos level in the 55th minute with a header from Giorgos Karagounis' inswinging corner, but Joseba Llorente fired Villarreal back ahead after another neat attack.