Smith followed up his stunning twin centuries at Edgbaston with a fluent 92 in the first innings of the second Test before being forced to withdraw from last day's play after receiving a nasty blow to the neck and head from a Jofra Archer bouncer.
Despite having been banned from the game for a year following his principal role in the disgraceful ball-tampering scandal, Smith has narrowed the gap with table-topper Virat Kohli, trailing him by a small margin of nine points.
However, the dependable batsman's fitness is doubtful as his concussion injury might rule him out of the third Test at Headingley, depriving him of the chance to better his outstanding record against the familiar foes.
Meanwhile, India is set to clash against the West Indies in the longest format for a two-match series beginning on Thursday, providing Kohli the opportunity to consolidate his hold over the No.1 ranking.
Australia's premier pacer Pat Cummins strengthened his dominant position in the rankings for bowlers as he sits atop the distinguished list with 914 points to his name.
Cummins' impressive tally of points is the fifth-most ever achieved by any bowler in the history of cricket.
Steve Smith is just nine ranking points away from being World No.1 Test batsman ?????? pic.twitter.com/PibunO1elF— Cricingif (@_cricingif) August 19, 2019
He is also ranked at No.5 in the rankings for all-rounders after delivering handy contributions with the bat lower down the order.
Elsewhere, Archer has announced his arrival in the ICC Test Rankings for bowlers at No.83 after a ravishing debut performance where he almost led his side to an unlikely win.
Ben Stokes has been rewarded for his unbeaten century in the Lord's Test as he jumped six spots to No.26 with Johnny Bairstow (No.30) and Rory Burns (No.64) also experiencing a rise in their positions.
Sri Lanka captain Dimuth Karunaratne displayed a superlative batting effort that saw him rack up 122 runs in his side's successful chase of the target of 268 and this has helped him break into the top ten reaching a career-high ranking of No.8.
Akila Dananjaya, making his comeback to Test cricket after a gap of several months due to his bowling action being declared dubious by the ICC, claimed six wickets in Sri Lanka's triumph and has leaped to No.36, progressing nine spots in the list.