The home side came the closest to breaking the deadlock in the first half when Mohamed Sissoko hit a post as they booked a tie against Fulham in the last 16.
Ajax lacked incision in attack as they failed to trouble Juve goalkeeper Alex Manninger.
Roma were the only other Italian team left in the competition but they are now out after losing 3-2 to Panathinaikos.
Djibril Cisse scored twice for the Greeks, who also won the first leg 3-2, either side of Sotiris Ninis' strike in the final five minutes of the first half.
John Arne Riise and Daniele De Rossi scored Roma's goals and Pana had a man sent off in the last minute, Kostas Katsouranis collecting a second yellow card.
Pana now face Standard Liege, who progressed 3-2 on aggregate after their second leg away to Salzburg also ended in stalemate.
Liverpool's next opponents will be Lille, after Adil Rami's late header saw the French side past Fenerbahce.
Emre Belozoglu's first-half strike would have seen Fener progress on away goals, with the tie locked at 2-2, but Rami popped up four minutes from time to reward Lille's pressure.
Valencia overturned a 1-0 first-leg deficit to see off Club Brugge in extra time.
Juan Mata needed only 13 seconds to level the tie from Luis Miguel's cross, but the Mestalla outfit had to wait a further 96 minutes for Pablo Hernandez's 20-yard winner.
The same player then forced two superb saves from keeper Stijn Stijnen before adding a late third from close range.
Claudio Pizarro's hat-trick earned Werder Bremen a tie with Valencia as a 4-1 win was more than enough to bounce back after losing 1-0 at FC Twente.
Naldo scored the Bundesliga side's other goal, with Luuk de Jong on target for Steve McClaren's side.
Hamburg saw off PSV Eindhoven on away goals after a dramatic finish.
PSV trailed 1-0 from the game in Germany but took the lead courtesy of goals from Ola Toivonen and Balasz Dzsudzsak.
But Mladen Petric and Piotr Trochowski put Hamburg back on top and Danny Koevermans' last-minute header was not enough for the hosts.
Anderlecht are next up for the German side after they produced a superb second-leg display to beat Athletic Bilbao 4-0, and 5-1 on aggregate.
Romelu Lukaku's strike gave them a fourth-minute lead which was extended by Mikel San Jose's own goal, with second-half strikes from Mbark Boussoufa and Jonathan Legear putting the gloss on the result.
Diego Forlan's last-minute winner saw Atletico Madrid past Galatasaray, a 2-1 win on the night sealing a 3-2 aggregate scoreline.
Simao's opener was quickly cancelled out by Kader Keita's header but, after Gala's Caner Erkin was sent off for two bookings within a minute, Jose Antonio Reyes set up Forlan to stave off extra time and settle the tie.
They now face Sporting Lisbon after the Portuguese side knocked out Everton.
Wolfsburg were another German side to enjoy a good night, winning 4-1 to complete a 6-3 aggregate rout of Villarreal.
Edin Dzeko, Christian Gentner and Grafite were on the mark, while Lopez Angel's own goal helped the Wolves on their way. Joan Capdevila scored for the Spanish side.
The reward for the Bundesliga side is a tie with Rubin Kazan after the Russians held Hapoel Tel Aviv to a goalless draw in Israel to preserve their 3-0 first-leg lead
Marseille, who face Benfica in the last 16, beat Copenhagen 3-1 for the second week in succession, Bakari Kone scoring twice after Hatem Ben Arfa had opened the scoring for the evening. Ailton scored Copenhagen's late consolation.
JUVENTUS BOOK FULHAM TIE
