The 33-year-old unorthodox southpaw from Guyana, who scored 442 runs at an average of 147.33, moved ahead of Ponting and Mike Hussey of Australia in the rankings and now sits just three points behind numero uno Kumar Sangakkara (938 pts), who claimed top-spot owing to indifferent form of Michael Hussey.
Sangakkara too will have another opportunity to impress, as Sri Lanka plays host to India during July and August.
Still making his way in Test cricket, 22-year-old Xavier Marshall is the biggest mover of the week, progressing 54 places to 82nd position, following his fine knock of 85 in West Indies' second innings.
Another positive to come out of the latest rankings for the West Indies is Jerome Taylor and Fidel Edwards, who moved up one and two places to 12th and 38th respectively in the rankings for Test bowlers.
The bowling rankings are still headed by spinner Muttiah Muralitharan making it a batting and bowling double for Sri Lanka, with South Africa's Dale Steyn in second and Australia's Stuart Clark closing the gap at the third position.
India and Sri Lanka ranked second and fifth respectively will look to improve their points tally when they take on each other in the three-Test series starting next month.
India (111) and England are locked at the same number of points on the ICC charts, but Anil Kumble's side just sneaks past Michael Vaughan's team, when the points are calculated beyond decimals.
Meanwhile, Australia, who are leading the rankings, were given a good competition by the West Indies, even though, Ricky Ponting's side managed to win the series 2-0.
ICC Test Rankings (teams):
1) Australia (141 pts), 2) India (111), 3) England (110), 4) South Africa (109), 5) Lanka (106), 6) Pakistan (94), 7) New Zealand (88), 8) Windies (77) and 9) Bangladesh (01).
*Zimbabwe has a rating of 12 but has not played sufficient number of Test matches over the new rating period to be included on the main table.