Liverpool's Dirk Kuyt is mobbed by team-mates after scoring the crucial winner for Liverpool.
Premier League sides Manchester City and Liverpool both took victory at home on Thursday, reaching the last 16 in the Europa League.
Man City were held 0-0 in the first leg away match against Aris Salonika, but dominated the home game with a 3-0 win over their Greek opponents.
Liverpool were also held to a goalless draw when they visited Sparta Prague in the first leg, and they couldn't split with the physical strong squad until Dirk Kuyt headed in a late winner.
At Eastlands, Italian boss Roberto Mancini sent a three-pronged attack of Edin Dzeko, Mario Balotelli and Carlos Tevez and got rewarded soon.
Aris player Nikos Lazaridis failed to get control of Aleksandar Kolarov's long pass, allowing Dzeko to open the score with a clinical right-foot finish in the seventh minute. The 27 million pound January signing striker added a second only after five minutes as he curled home with his left foot.
The hosts were likely to score more but had to wait until the 75th minute to gain a third when Yaya Toure's long-range shot deflected into net.
Man. City will meet Dynamo Kiev in the last 16 round after the Ukrainian side knocked out Besiktas 8-1 on aggregate.
Ealier at Anfield, the Reds fought hard with the absence of their captain Steven Gerrard and were finally rewarded a last 16 berth with Dutchman Kuyt's header in the 86th minute.
Liverpool will next play Braga who beat Lech Poznan 2-1 on aggregate.
