Fifth seed Nishikori goes on to face either Czech fourth seed Tomas Berdych or Jo-Wilfried Tsonga, the 14th seeded Czech, for a place in the semi-finals.
Jiro Satoh was the last Japanese man to enjoy such a run in Paris when he went on to the semi-finals in 1931 and 1933.
Nishikori hadn't played since Wednesday after scheduled third round opponent Benjamin Becker withdrew with an injury.
The 25-year-old looked the fresher of the two out on a damp, chilly Court Suzanne Lenglen dominating the first set and racing to a 5-1 lead in the second before 74th-ranked Gabashvili briefly rallied with a face-saving break in the eighth game.
Gabashvili saved two match points but the Japanese, who had beaten the Russian in Barcelona in April on his way to a successful defence of his claycourt title, won through.
Nishikori finished with 40 winners, more than three times his opponent's and took his clay record this year to 13-2.
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