The former Chelsea forward, who left French club Lille in August, scored in each half to take his goal tally to three in the league and establish himself as the leader of the attack.
Moritz Leitner netted from three metres for Stuttgart after a brilliant back-heel from Vedad Ibisevic had sent Florian Klein racing down the wing in the fifth minute.
Ivory Coast international Kalou then tested visiting keeper Thorsten Kirschbaum's reflexes with a low drive in the 21st minute.
The keeper again did well to deny Valentin Stocker a minute later but the Swiss was brought down by Carlos Gruezo and Kalou sent Kirschbaum the wrong way with his penalty.
The 29-year-old, who won the Champions League with Chelsea in 2012, has quickly adapted to the Bundesliga, giving Hertha much-needed punch up front following the departure of Adrian Ramos.
Kirschbaum stopped a spectacular volley from Roy Beerens on the stroke of halftime but could do nothing when Kalou raced into the box, shook off a defender and slotted past the on-rushing keeper in the 63rd minute.
Beerens made sure of victory, scoring 11 minutes later following a fine Anis Ben-Hatira cross, before Sandro Wagner's 84th-minute own goal set up a nervous finale.
Hertha have eight points from seven games while Stuttgart are fourth from bottom on five points.
Leaders Bayern Munich take on Hanover 96 on Saturday when last season's runners-up Borussia Dortmund are desperate for a win against Hamburg SV.
(Reporting by Karolos Grohmann, editing by Tony Jimenez)
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