The lone English club left in the tournament managed only half the number of Benfica's 22 attempts on goal at the Stadium of Light, and it scored against the run of play.
Kalou tapped in Fernando Torres' cross from the right in the 75th minute of the first leg of the quarterfinals to give Chelsea the advantage ahead of the Stamford Bridge match on April 4.
Chelsea was coming off a 2-1 loss at Manchester City last week and a 0-0 home draw with Tottenham, leaving the team in fifth place in the Premier League and outside the automatic qualification places for next season's elite European club tournament.
On Tuesday in Lisbon, Chelsea defended well but created few chances other than Juan Mata hitting the post from a wide angle in the 61st after a defensive blunder.
"We were solid defensively and well-organized against a good team," Chelsea interim manager Roberto Di Matteo said. "We haven't qualified yet. It's dangerous to think we're through ... We've put ourselves in a good position, but it's not a result you can rely on for the home game."
It was the first loss in 11 European home games for Benfica, which is aiming to make its first semifinal appearance in the tournament in 22 years.
"We didn't deserve to lose here today. We were the best team for most of the game, we produced most of the chances," Benfica coach Jorge Jesus said. "We're not out yet. We can still turn this around."
Di Matteo recalled Fernando Torres and David Luiz on Tuesday in place of Didier Drogba and Gary Cahill, who both started against Tottenham last weekend. Frank Lampard was also on the bench.
Benfica made most of the running, with Chelsea mostly content to slow the pace.
Benfica striker Oscar Cardozo rose above two defenders but headed weakly at goalkeeper Petr Cech in the 15th. He soon had a better opening, running into the area and receiving the ball on his chest before hitting a volley wide.
Benfica lacked composure in front of goal, with Bruno Cesar's 32nd-minute shot the first on target.
Ramires, a former Benfica player, kept outpacing left back Emerson, but Torres — who recently ended a career-worst goal drought of 26 games — couldn't convert the possession he received into clear chances.
Midfielder Raul Meireles' low drive just before the interval forced goalkeeper Artur to dive sharply to his right in Chelsea's best first-half effort.
Benfica cranked up the pressure after the break. Cardozo's close-range shot looked to be going in but it hit Luiz on the chest, and Jardel's header forced a reflex save from Cech.
Chelsea captain John Terry was repeatedly called into action, blocking Alex Witsel's shot then cutting out Rodrigo's pass to Cardozo that would have put him through on Cech. Lampard came on for Meireles, but Chelsea still looked the less likely victor.
But when Torres beat Jardel on the right flank, Kalou just needed to side-foot the ball into the net for the winner.