Thomas Müller netted a 50th-minute penalty for Germany only for Georgia captain Jaba Kankava to make up for conceding the spot kick by hitting a superb equaliser, but Kruse then came off the bench to claim the late winner.
The result saw Germany finish top of the table by a point, while Poland join them in qualifying directly for the finals in France after their 2-1 win over the Republic of Ireland in Warsaw.
But Germany's victory in Leipzig did little to disguise the world champions' below-par campaign over the last 12 months and head coach Joachim Löw admits there is huge room for improvement.
With the scores locked at 1-1 mid-way through the second-half, Georgia threatened to inflict a second embarrassing defeat on Germany, who had succumbed to a 1-0 loss to Ireland in Dublin last Thursday.
Today we can sing the same song from the Ireland match,” fumed Löw.
“We missed three or four very clear chances in the first half and a certain frustration comes when errors creep in.
“We are generally satisfied that we have managed to qualify, but dissatisfied with the last two games.
“That is not our standard, there is still much work ahead of us.”
After away defeats to both Poland and Ireland, this has been Germany's worst qualifying campaign for a major tournament since the 2002 World Cup when they finished second behind England in their group.
They were made to work in Leipzig by a battling Georgia team who finished second from bottom in the table.
Both sides had first half chances as Marco Reus and Müller went close while Georgia's Tornike Okriashvili forced Germany goalkeeper Manuel Neuer into a stunning save on 27 minutes from 12 metres out.
Germany looked to have the game under control when Mesut Özil was sent sprawling by Kankava early in the second half as Müller stepped up to slot home the resulting penalty.
But Kankava instantly made amends when the midfielder chested down a poor headed clearance from Jonas Hector and unleashed a rocket of a volley into the top right-hand corner on 53 minutes.
It sent the small pocket of watching Georgia fans into ecstasy and suddenly Germany's direct qualification looked far from assured.
Another Hector mistake gave midfielder Valeri Kazaishvili a half chance on 57 minutes from which he drew another top save from Neuer.
But Wolfsburg's Kruse came off the bench on 76 minutes to spare Germany's blushes.
The 27-year-old had been on for just 150 seconds when he collected Özil's final pass and slammed his shot home.
The winner nudged Germany into life and although they created further chances, Löw will demand his attack finishes more chances in November's friendlies against France and the Netherlands.
“In training, we shoot 50 goals and ball after ball flies into the net,” said a bemused Neuer when asked about Germany's poor finishing.
“We need the killer instinct up front and we're making life hard for ourselves when we also concede the equaliser.
“Hopefully, we'll be different for the European championships and will re-find our game, which the German national side is known for.”