Wet and windy conditions acted as an unwanted leveller for the Georgians as Scotland had to rely on the boot of Dan Parks to see them home.
The Cardiff Blues fly-half, who was one of the 11 changes from the side that won Saturday's opener 34-24, slotted four penalties and a well-taken drop goal to send Scotland further ahead at the top of Pool B.
Defensively Scotland were hugely impressive, just as they were up front against a Georgian pack known for their aggression and physicality, particularly at the setpiece. But the Scots struggled out wide, with the backline rarely sparking into action as the Georgian tryline remained largely untroubled.
But despite his side's failure to cross the whitewash or pick up a try-scoring bonus point, Robinson insisted he was more than happy with the outcome.
"Some days you've got to play this way - you've got to win ugly," said Robinson, whose squad have now 11 days off after facing two games in four days.
"The key for us was to win the game. I was delighted with the way the players played, right across the board.
"I set the target when we discussed the first phase of our campaign that when we left Invercargill we wanted nine points. We've achieved that and the guys stuck to a very good plan today.
"I thought the front five were outstanding in the way they took on the renowned Georgian pack."
Next up for Scotland is a crucial clash with Argentina on September 25 before finishing the group stages with a mouth-watering match against England on October 1.
Scotland have never failed to qualify for the knockout matches in six previous World Cups and their two wins in this year's competition stand them in good stead ahead for the big games to come.
They head to Wellington for the game against the Pumas on the back of five successive victories, having disposed of Italy (twice) and Ireland earlier this year before the wins over Romania and Georgia.