Smith has a chance to cement his place at the top in the fourth Ashes Test, which starts at Old Trafford on Wednesday.
Virat Kohli became India's most successful Test captain after the team thrashed West Indies in the second match of series by 257 runs in Jamaica on Monday.
Set the improbable target of 468 late on day three, the home side tumbled in the post-lunch session, losing their last six wickets for 51 runs as they were dismissed for 210 to hand Virat Kohli's side a clean sweep of a Test series in the Caribbean for the first time ever.
He had sat out Australia's third Ashes Test defeat at Headingley after suffering concussion when he was struck by a vicious bouncer from Jofra Archer at Lord's.
Among others, Ajinkya Rahane returned to top 10, rising four places to No.7, after following up his half-century and hundred in Antigua with another useful fifty in Jamaica.
Former captain Smith has not held top spot in the rankings since December 2015.
Sharma, who didn't get to play either of the Tests, would now be looking forward to the upcoming T20I series against South Africa at home.
"I think the find of the series has to be Hanuma Vihari", Kohli added.
In ICC Test rankings for bowlers, Bumrah, who is now the No.1 ODI bowler, continued his impressive run to climb up to the third spot with a career-best 835 rating points.
Jasprit Bumrah and Jason Holder have risen into the top five of the Test bowling rankings, with Bumrah up from seventh to third and Holder moving from 11th to fourth. India bowled West Indies out for 117 and then scored 168 for 4 declared in their second innings.
He is now only behind Australia's Pat Cummins and South Africa's Kagiso Rabada.
Bumrah finished as the leading wicket-taker in the series with 13 dismissals at an exceptional average of 9.23, which follows his impressive performance at this year's World Cup.
With Bravo and Blackwood both batting in the same innings, it gave West Indies the first 12-batsman Test scorecard under the protocol.