Wales international Robinson was in excellent form with the boot
Fly-half Nicky Robinson scored all of Gloucester's points to reignite their push for a top-six finish and end Leeds' three-match winning run.
The Wales international scored the only try in the 68th minute when he beat Hendre Fourie to touch down his grubber kick from the 22-metre line.
Robinson converted the try, as well as kicking 12 points with four penalties.
But the hosts lost Mike Tindall, back from England duty, to injury when the centre limped off after six minutes.
The 31-year-old, who impressed in England's Six Nations defeat by France in Paris last week, only recently returned to fitness following a hamstring injury.
Gloucester boss Bryan Redpath switched James Simpson-Daniel to centre, but the Cherry and Whites missed Tindall's influence in midfield.
While the victory extended Gloucester's unbeaten home run to nine matches, the hosts were forced to soak up early pressure as prop Juan Gomez and Fijian Seru Rabeni came within inches of the tryline.
But the visitors were guilty of conceding kickable penalties inside their own half, allowing Robinson to slot over three kicks to give Gloucester a 9-0 half-time lead.
Robinson extended the lead to 12 points just 40 seconds after the interval, but Gloucester suffered a second injury blow when skipper Gareth Delve limped off in the 47th minute with an ankle problem.
Leeds began to unravel as fly-half Ceiron Thomas missed a long-range penalty on the hour.
And Robinson settled the result 12 minutes from time when he beat Fourie to the touchdown from his clever kick, adding his 19th point when he converted his own try.
The victory leaves Gloucester six points behind West Country rivals Bath in seventh place in the Premiership.
Gloucester head coach Bryan Redpath:
"It was a decent win and four points against a side which has not lost in five games.
"They have been pretty dogged and we knew that would be the case so we had to work to win the game.
"Nicky kicked fairly well today and his try was good vision to take the chance. He worked well too."
Leeds head coach Neil Back: "We created a lot of chances but we have to support our line-breaks better. The fact that we are creating them is positive but we didn't take those opportunities.
"We have played top Premiership clubs in the last four games - Leicester, Saracens, Sale and Wasps - and we have been dominant in the scrum.
"We have been heavily penalised in that area today so I was a bit confused.
"And the fact that the penalty count was 15-2 until the last 15 minutes meant again I was confused with a lot of those decisions. But, as normal, we will go through the process of requesting that Tony Spreadbury (the match referee assessor) goes through the game and, hopefully, he can give some answers."
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