"It was everything we wanted it to be. We knew it was going to be a tough game and they hardly threatened," Chelsea midfielder Frank Lampard said. "It was a very controlled, very professional performance from all of us."
In the night's other match, Cristiano Ronaldo scored twice in Real Madrid's 3-1 victory at home over Schalke, finishing a 9-2 rout in the home-and-home, total-goals series.
England failed to have a quarterfinalist last year in Europe's top club competition for the first time since 1996, and Arsenal and Manchester City were eliminated last week. On the final night of the second round Wednesday, Manchester United will try to overturn a 2-0 deficit when it hosts Olympiakos.
Borussia Dortmund has a 4-2 lead going into Wednesday's game against visiting Zenit St. Petersburg and new coach Andre Villas-Boas. Defending champion Bayern Munich, Barcelona, Atletico Madrid and Paris Saint-Germain reached the quarterfinals last week.
The draw is Friday,
"I think all of the best teams have won their series, although there can be some surprises," Madrid coach Carlo Ancelotti said. "Whoever we draw, it's going to be difficult."
Galatasaray forward Didier Drogba made no impact as he played at Stamford Bridge for the first time since leaving the Blues at the end of the 2011-12 season, when his penalty kick during a shootout beat Bayern Munich in the Champions League final.
Eto'o scored from a tight angle in the fourth minute, and Cahill doubled the lead from close range in the 42nd.
In Madrid, Ronaldo scored in the 21st and 74th minutes, giving him 13 Champions League goals this season — one shy of the Champion Clubs' Cup/Champions League record shared by AC Milan's Jose Altafini (1962-63) and Barcelona's Lionel Messi (2011-12).
Ronaldo has 41 goals overall for Madrid this season, reaching the 40-goal mark for the fourth straight season. With 242 goals for Real, he tied Ferenc Puskas for fourth on the club career list behind Raul Gonzalez (323), Alfredo Di Stefano (305) and Carlos Santillana (289).
Schalke's Tim Hoogland scored on a shot that deflected past goalkeeper Iker Casillas in the 31st, and Alvaro Morata got Madrid's final goal in the 75th. Gareth Bale assisted on the first and third goals for Real.