Smith surpassed New Zealand captain Kane Williamson to reach the second spot. Smith is now just nine points behind Kohli (922) points.
The 30-year-old Smith scored 378 runs across three consecutive innings in the ongoing Ashes series in England. On the other hand, Kohli is yet to get a chance to better his lead as India gear up to face West Indies in the two-match series, starting from August 22.
England all-rounder Ben Stokes bettered his ranking by six places to achieve the 26th position while wicketkeeper-batsman Jonny Bairstow moved seven places to take the 30th spot.
Sri Lanka captain Dimuth Karunaratne, who played a match-winning knock of 122 against New Zealand at Galle, climbed four places to the 8th position.
England bowlers Stuart Broad and Chris Woakes gained two places in the bowler's list, and are currently positioned at the 14th and 27th spots respectively. Pacer Jofra Archer also entered the rankings and was placed in 83rd position after ending up with five wickets in his debut Test.
In the bowlers' rankings, Australia's Pat Cummins retained the top spot.
In terms of team rankings, India are at the pole position, but they can lose their spot if the side loses 0-1 against the Windies.