The capital club are now unbeaten in eight games after the narrow win and move second in the Serie A table.
Lazio stretched its undefeated run to eight games after an entertaining 1-0 win over Parma at the Stadio Olimpico in Rome. A Giuseppe Scullli strike six minutes from time earned the points for the hosts, and move second in the table as a result of their triumph.
The Biancocelesti were in trouble in the first minute as Federico Marchetti failed to deal with a Stefano Morrone effort but Mobido Diakite came to the keeper's rescue.
Adboulay Konko might have done better when found in space on the edge of the area by Cristian Brocchi but neither shot or crossed, much to the frustration of Cisse. Hernanes forced a smart save from Antonio Mirante after Brocchi won a free-kick 20 yards out, then from another corner Bosnian midfielder Senad Lulic hit the bar with Mirante rooted to the spot.
After weathering the storm, Parma regained composure in the centre and had a chance to take the lead when Graziano Pelle was played in but the 26-year-old was challenged by Diakite.
Moments before the break Jonathan Biabany was inches away from his first goal for the club since getting the winner against Juventus in May 2010. The Frenchman's header smashed the crossbar with Marchetti beaten.
Talisman Sebastian Giovinco came off at halftime after picking up an injury and was replaced by Francesco Valiani, and the tempo dropped in the second half, as Parma proved more resolute and compact in defense.
Center-half Cristian Zaccardo had the best chance in the 75th minute, making a smart turn at the back of the area before slashing his shot well wide from seven yards.
The game appeared to be heading for a draw as Hernanes made way for Uruguayan midfielder Alvaro Gonzalez, and Czech forward Libor Kozak came on for only his second appearance in Serie A.
However, with six minutes left on the clock Klose burst forward on the right to feed Kozak in space. The 22-year-old's shot came back off the post but Sculli prodded home as the ball trickled across the line.
The defeat was Parma's third in four matches and Franco Colombo has much to ponder as Serie A pauses for next week's international break.
Reja's side is unbeaten in eight games with six wins and climb up to second, but the FIFA friendlies could prove a headache with a number of his squad involved and crucial games against Napoli and Juventus to come.