Die Roten had previously lost to Mainz and Ausburg on their travels in a run of three consecutive defeats at the start of the season, but Genter's header just after the break secured them a second straight win following their home success over Hoffenheim.
Adrian Ramos created an early opening for the hosts, but he blazed over the crossbar on 25 minutes from the left side of the penalty area.
Gentner showed his aerial capability just prior to the interval when he rose highest to meet an Alexandru Maxim cross, only for Thomas Kraft to keep Hertha on level terms.
The Berlin defence did not address Gentner's threat from set pieces after the break, as the Stuttgart skipper powered a thumping header from Maxim's corner beyond Kraft on 49 minutes.
However, the hosts nearly equalised moments later when Hamburger SV loanee Per Ciljan Skjelbred's effort from Ramos's cross was well blocked by Stuttgart keeper Sven Ulreich.
Ulreich saved well from Johannes van den Bergh and substitute Sandro Wagner later in the action as the visitors hung on, inflicting a second successive defeat on Hertha in the process.