Reja was making his second debut on the Lazio touchline after the much publicised sacking of Vladmir Petkovic. Just like he did in last season's corresponding fixture, Klose netted the decisive strike to give Lazio a fourth consecutive victory over Inter Milan.
Lazio end a barren run of just one win in eight domestic games, while Walter Mazzarri tastes defeat for the third time as Inter coach.
Ricky Alvarez returned from suspension for the visitors, but Hugo Campagnaro sat out a ban, while Cristian Chivu and Saphir Taider were injured. Flu victim Mauro Icardi was on the bench, along with Diego Milito, who had endured an injury ravaged 2013.
Chances were few and far between during the early stages. Juan Jesus sent the first noteworthy effort over for the visitors. A miscommunication in the Inter defence almost let Lazio in. Jonathan and Andrea Ranocchia allowed the ball to run and Samir Handanovic was late running out, allowing Senad Lulic to loft the ball over his head and wide of the far post.
Juan Jesus was caught in possession by Antonio Candreva, but the defender refused to let the Lazio winger break clear and won back possession in his own half. Alvarez failed to test Berisha from a set piece, sending his free kick over the bar midway through the first half.
Handanovic rushed out to punch clear a Cristian Ledesma free kick, stopping Klose from pouncing. The veteran forward just missed sliding onto Candreva's deflected ball moments later, with Handanovic clearing the danger once more.
Lazio created a couple of chances after half an hour. Lulic cushioned a header down for Hernanes to turn wide, before Candreva stung Handanovic's gloves with an angled drive.
Fredy Guarin and Radu picked up costly yellow cards for a brief skirmish, stemming from a foul on Lulic. Both players will now be suspended for next weekend's games. A minute before the interval, Juan Jesus played a poor backpass, forcing Handanovic to run out and boot clear from the advancing Candreva.
Defences were on top after the restart. A last ditch challenge from Giuseppe Biava prevented Rodrigo Palacio from pulling the trigger, while Berisha palmed Yuto Nagatomo's header onto the roof of the net.
Hernanes showed a flash of pace, as he broke with the ball and released Candreva. A poor first touch from the Lazio man gave Juan Jesus the chance to take the ball and clear the danger. Candreva tried to pick out Klose at the back post, but his ball was just a yard ahead of the frontman.
Milito replaced the ineffective Guarin for the final 15 minutes to try and give the Inter attack some more bite. However, it was Lazio that struck the crucial blow nine minutes from time after some good build up play. Cavanda took the ball past Nagatomo and laid it off to Candreva. The Italian international sent a first time cross into the box and Klose got in front of Ranocchia to volley the ball past Handanovic from six yards.
Mateo Kovacic sent a snapshot wide in the final minute, while Juan Jesus denied Klose a second with the last kick of the game.
Lazio: Berisha; Konko, (Cavanda 15) Biava, Dias, Radu; Candreva, (Ederson 88) Gonzalez, (Onazi 62) Ledesma, Hernanes, Lulic; Klose
Inter: Handanovic; Ranocchia, (Zanetti 83) Rolando, Juan; Jonathan, Kuzmanovic, (Kovacic 60) Cambiasso, Alvarez, Nagatomo; Guarin; (Milito 75) Palacio
Goals: Klose 81 (L)