In doing so, Lazio ended a run of five successive defeats against AS Roma, four in the league and one in the cup, the last four of them under coach Edoardo Reja.
Pablo Osvaldo gave Roma an early lead before Hernanes levelled early in the second half with a controversial penalty which also resulted in Roma's Simon Kjaer being sent off.
Juventus and Udinese stayed level at the top of Serie A after Juventus's visit to Chievo and Udinese's trip to Atalanta were among the 0-0 draws.
Cesena captain Adrian Mutu was sent off for elbowing against his former team Fiorentina, where he spent five seasons before joining the Sea Horses in the summer, in another goalless match.
Genoa and Lecce also failed to hit the target as did third-placed Cagliari and Siena, while Bologna won 2-0 at Novara.
Juventus and Udinese, both unbeaten, stayed level at the top with 12 points apiece from six games, with Juve enjoying the better goal difference.
Cagliari and Lazio are a point behind in third and fourth place and one ahead of Napoli and Palermo. Napoli lost 2-1 at home to Parma on Saturday when Palermo were drubbed 3-0 at AC Milan.
The drama was saved for the evening as Argentine-born Italy forward Pablo Osvaldo burst through to fire Roma ahead after only five minutes at the Olimpico.
Lazio levelled six minutes after the break when Kjaer brushed Cristian Brocchi who went sprawling theatrically in the area and celebrated as if he had scored the title-winning goal when the referee pointed to the spot.
Kjaer was sent off and Brazilian playmaker Hernanes coolly converted the penalty.
The remaining 40 minutes were action-packed as Lazio pushed forward and depleted Roma attempted to counter.
Klose headed against the bar and Djibril Cisse hammered a volley against the foot of the post for Lazio as Roma appeared set to hold on for a draw.
However, Germany forward Klose made up for a series of misses - firing one effort over from 10 metres with the goal at his mercy-- by scoring with virtually the last kick.
Matuzalem found Klose with a cleverly flicked ball and he held off his marker and coolly slotted the ball home to spark wild celebrations.
Juventus were fortunate to salvage a point following a controversial decision to disallow Cyril Thereau's 20th-minute strike for Chievo for an alleged foul on Andrea Pirlo.
To add insult to injury, Thereau was booked for playing on after the whistle.
Chievo also had a penalty turned down in the second half when Sergio Pellissier appeared to be tripped, while substitute Alessandro Del Piero had Juve's best effort when he headed against the post.
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