This comes after West Indies suffered a 3-2 series loss to Bangladesh in the five-match series which ended on Saturday in Dhaka.
Narine’s movement was driven by his success in the series where he picked up nine wickets at an average of 21.55.
The right-armer took three for 38 in Saturday’s final ODI which the Windies lost by two wickets in a tense finish at the Sher-e-Bangla National Stadium.
Fast bowler Kemar Roach also saw progress in the rankings, returning to the top 20 at 18th after jumping five places. He was lifted by his five-wicket haul on Saturday.
Captain Darren Sammy, who took six wickets at 26 runs apiece with his medium pace, also moved up six places to 35th in the rankings.
Gayle, meanwhile, had a disappointing series with just 72 runs from five innings to lose ground in the standings.
The left-hander, who had a bumper series against New Zealand in the summer, had a high score of 35 in the opening game that Bangladesh won by seven wickets in Khulna.
There was no such misfortune for Darren Bravo who jumped 13 places to 50th after a consistent outing in the series that yielded 161 runs at an average of 32.
However, all-rounder Andre Russell and opener Lendl Simmons both suffered in the rankings as a result of their poor form in the series.
Russell, with nine runs from three innings including two noughts, fell ten places to 46th while Simmons, dropped after scoring just 22 runs in the first two ODIs, slipped four places to 44th.
