The hosts left it until late to take the lead at the Stadio Olimpico against Walter Mazzarri's men, with the German volleying in from close range.
The 68-year-old was confirmed as the successor to Vladimir Petkovic on Saturday and his return for a second spell in charge prompted a response from underachieving Lazio, with Klose's superb half-volley lighting up a largely uninspiring affair in Rome.
The Biancocelesti had the better of the first-half exchanges and Senad Lulic came closest with a lofted half-volley following confusion between Jonathan and goalkeeper Samir Handanovic.
Inter showed a marked improvement after the break, but rarely threatened the Lazio goal and was punished when Klose met Antonio Candreva's right-wing cross with a sweetly struck volley in the 81st minute.
While the result represented a blow to Inter, it was boosted by the return of Diego Milito - who has been absent for the better part of a year with knee and thigh injuries. Milito came on as a substitute for Fredy Guarin but was unable to prevent a defeat that leaves his side sixth, four places above Lazio.
Etrit Berisha made his Serie A debut in goal for Lazio as regular No. 1 Federico Marchetti was unavailable with a muscular problem. Ricardo Alvarez returned from a one-match suspension for the Nerazzurri.
Lazio looked more settled in the opening stages and Senad Lulic almost capitalized on confusion in the Inter box by lofting an effort just wide of the far post 10 minutes in.
The hosts were dealt a blow soon after when fullback Abdoulay Konko was carried off on a stretcher and replaced by Luis Cavanda. Inter enjoyed plenty of possession but struggled to break through a resolute Lazio defense, with an Alvarez free kick that curled wide the visitors' best effort.
Hernanes will feel he could have done better for Lazio on the half-hour mark when he scuffed an effort wide from Lulic's knockdown. Lazio applied more pressure at the end of the half and Cavanda stung the palms of Handanovic with a drive from the edge of the box.
Things remained tight in the second half, but it took a superb sliding challenge from Giuseppe Biava to deny Rodrigo Palacio when the forward looked to be through one-on-one with Berisha.
Inter continued to control the tempo and saw a fine chance go begging after 62 minutes. Jonathan burst down the right-hand side and crossed to the far post, where Yuto Nagatomo headed straight at Berisha. With 20 minutes remaining, Lazio almost went ahead against the run of play when Cavanda's centering feed narrowly evaded the head of Klose.
The Germany international made no mistake with nine minutes remaining, though, calmly guiding Candreva's inviting cross beyond Handanovic to delight the home faithful.
Klose could have had a second in injury time, but Juan got back to make a fine, last-ditch tackle.