Cagliari have enjoyed a promising run including a 4-1 win away at Inter Milan since wily veteran Zdenek Zeman took over the Sardinians at the start of the season.
However Lazio had won five of the sides` past six league meetings and after Victor Ibarbo saw red in the 72nd minute the hosts survived a brief, second-half fightback at the Olympic Stadium to claim their sixth win of the season.
Lazio are six points adrift of leaders and defending champions Juventus but only three points behind city rivals Roma, who lost 2-0 to Napoli on Saturday.
Lazio`s quickfire start was rewarded with a seventh-minute opener from captain Stefano Mauri, who bundled the ball past Alessio Cragno from close range as it ricocheted in the Cagliari box.
It was far from pretty, but Klose made amends on 25 minutes when Germany`s all-time record goalscorer fired past Cragno from close in after Senad Lulic had headed Antonio Candreva`s cross into the 36-year-old German`s path.
Klose, who retired from international football after helping Germany to World Cup glory in July, grabbed his second a minute later when he beat Cragno from the edge of the area with a slightly deflected shot.
Cagliari were given brief hope of a fightback when Dutch left-back Edson Braafheid deflected Andrea Cossu`s effort past Federico Marchetti in the Lazio net three minutes after the restart.
Ibarbo twice came close to opening his account but was stopped twice by an alert Marchetti and the Colombian was given his marching orders on 72 minutes when he lashed out following a tussle with Lulic on the left flank.
Zeman replaced midfielder Lorenzo Crisetig seven minutes later with Joao Pedro, and the Brazilian reduced arrears six minutes from the final whistle after beating Marchetti from close range.
Ederson came on for Mauri on 88 minutes and in the second minute of injury-time had the easiest of tap-ins past a stranded Cragno when Candreva`s inviting ball into the box duped the Cagliari defence.
Earlier, Verona grabbed a share of the points at Cesena and remained in 11th spot, 12 points adrift of Juve. Cesena`s fourth draw of the season left them third from bottom.