Roberto Di Matteo's Blues put in an accomplished performance at a tricky place to visit but came away with the goods, and an away goal, ahead of the return leg at Stamford Bridge on April 4.
Chelsea withstood a lot of pressure from Benfica for most of the second half and got their rewards for a composed showing in the 75th minute when Fernando Torres got himself free down the right before advancing into the area and chipping a deft ball into the path of Salomon Kalou who stabbed home from six yards.
Benfica had the better of the clearcut chances which started in the 18th minute when Oscar Cardozo's left-footed effort, after controlling in the area, was just wide of the mark.
Chelsea's best initial effort came in the 40th minute when Benfica keeper Artur came up with a brilliant save to deny a well-struck Raul Meireles effort before Cardozo struck on target from close range early in the second half but David Luiz was perfectly placed to deflect away with his chest prompting the Benfica fans to scream out for handball.
Benfica had really stepped up in the opening 10-15 minutes of the second term and they had another big call for handball on the hour-mark when Maxi Pereira's volley from the right side of the area struck the arm of John Terry but referee Paolo Tagliavento wasn't interested.
Moments later, Juan Mata managed to round Artur from Blues keeper Petr Cech's long ball but his first touch under pressure was way too heavy and his angled effort rocketed into the near upright.
In the 67th minute, Cech came up with another top save to deny Jardel's back post header from Nicolas Gaitan's left wing cross before a dangerous ball into the six-yard box from Gaitan, with a trio of Benfica players waiting, was cleared by Ashley Cole to help put the visitors well on their way to a final four tie.
UEFA Champions League quarter-finals - first leg
Estadio da Luz, Lisbon - 60,000