The 27-year-old seamer, who has played 62 Tests for his country, was England's biggest mover as he jumped four places to seventh after returning figures of six for 81 and two for 55 at the Gabba, while Chris Tremlett made a return to the bowling rankings in 32nd place.
Mitchell Johnson, the star of Australia's 381-run win, climbed back into the top 20 following an impressive return of four for 61 and five for 42 for which he was rewarded with a move of four places to 19th after his side claimed a 1-0 lead in the five-Test series.
Australia off-spinner Nathan Lyon, meanwhile, moved three places up the rankings to 18th position.
South Africa's Dale Steyn continues to head the bowlers' table with team-mate Vernon Philander second and Sri Lanka's Rangana Herath currently third.
Johnson, named man of the match in Brisbane, also recorded vital scores of 64 and 39 not out in each innings for Australia and his efforts with the bat saw him jump 20 places to 78th in the Reliance ICC rankings for Test batsmen.
Australia captain Michael Clarke moved up a place to fourth after hitting his 25th Test hundred when he scored 113 in the second innings of the Brisbane Test.
The 32-year-old gained 17 points for a total of 870 following his 97th Test for his country and sits just 39 points behind top-ranked AB de Villiers, while England captain Alastair Cook moved up a place to 10th.
Australia opener David Warner made a massive jump of 18 places up to 17th as he made it into the top 20 for the first time in his career after his impressive knock of 124 in the second innings at the Gabba.
And his team-mate, wicketkeeper Brad Haddin, was the only batsman outside the top 20 to move up as he climbed 14 places to 42nd.