The German forward struck nine minutes from time to hand Lazio a deserved 1-0 victory in their first game of 2014.
Lazio, who had won just one of their last eight league matches heading into the contest, decided to sack Vladimir Petkovic at the weekend.
The victory has lifted the Romans to 10th place while it has left Inter in sixth, eight points behind third-top Napoli.
The only positive for the visitors was the return to play of Diego Milito after a three-month injury absence.
The Argentinian forward played the last 15 minutes.
The visitors went into the game at the Stadio Olimpico on the back of a 1-0 win in the Milan derby.
Lazio, who were without injured goalkeeper Federico Marchetti, were the better side in the opening half and almost went ahead in the 11th minute.
Senad Lulic was quick to get to a loose ball in the Inter area and beat goalkeeper Samir Handanovic only to see his attempt go inches wide of the far post.
The hosts were forced to make their first substitution in the 15th minute with Luis Cavanda replaced an injured Abdoulay Konko.
The visitors struggled to put a good move together until midway through the first half when Ricky Alvarez's free-kick went over the bar.
In the 35th minute, Antonio Candreva warmed the palms of Handanovic with a bullet strike from just outside the area.
On the stroke of half-time, Handanovic was forced to clear following a dangerous back-pass by defender Juan Jesus with Klose threatening.
Inter began to look more dangerous and had a good chance to break the deadlock shortly after the hour mark with Yuto Nagatomo's header from Jonathan's cross forcing Lazio goalkeeper Etrit Berisha to make a save.
Shortly after Milito stepped onto the pitch to replace Fredy Guarin, Lazio scored.
Candreva's cross found Klose in the heart of the area and his powerful right-footed strike beat Handanovic.
Lazio defended deeply and the closest Inter came to equalising was deep in stoppage time when substitute Mateo Kovacic's long-range attempt went wide of the far post.