The Ivory Coast frontman was one of seven changes in the Pompey ranks and repaid the faith shown in him netting in the first half before turning provider in the second.
Dindane cancelled out former Leeds defender Ian Harte's early penalty in the 26th minute, before fellow striker Danny Webber fired Portsmouth in front minutes later.
Pompey's only other win this season came against Hereford in the previous round of the Carling Cup and Dindane set up Anthony Vanden Borre in the 63rd minute to make a second victory certain.
Hart's troops are yet to pick up a point in the Premier League this season and their woes looked set to continue as early as the third minute.
South African Aaron Mokoena had a rush of blood to the head bringing down Carlisle's Joe Anyinsah as he broke into the Portsmouth box with Harte making no mistake from the spot.
However, the visitors quickly put that to one side with Dindane showing glimpses of what was to come firing just wide in the 12th minute.
Carlisle had a series of corners shortly after but couldn't make the pressure count as Dindane pulled Portsmouth level after tapping home from close range following good work from John Utaka.
The visitors wasted little time in doubling their advantage and were in front six minutes later when Webber rose highest to flick Hassan Yebda's cross home.
Carlisle tried to battle back but were no match for a rejuvenated Portsmouth with Vanden Borre putting the clash beyond doubt after linking up with Dindane in the 63rd minute.
The Cumbrians threw men forward and Mokoena nearly made the same mistake twice after hauling down former Millwall striker Scott Dobie on the edge of the box in the 77th minute.
However, Harte failed to convert the free-kick like he did the penalty as Portsmouth held on and temporarily lifted the pressure on manager Hart.