Moeen's second-innings haul of 6 for 53 completed career-best match figures of 10 for 112, as South Africa were bowled out for 119 on the fourth day to succumb to a 211-run defeat. That effort followed a vital 87 from 147 balls with the bat in the first innings, as Moeen helped add 177 for the sixth wicket with Joe Root and drive England towards a healthy total of 458.
His efforts meant he became the fifth-fastest player to reach 2000 Test runs and 100 wickets, as well as the first for England to score a fifty and record a ten-wicket haul in the same match since Ian Botham in 1980.
As a consequence, Moeen has achieved career-best batting, bowling and allrounder marks in the latest ICC player rankings, and is now considered the third-best allrounder in the world, behind Bangladesh's Shakib Al Hasan and India's Ravindra Jadeja, with Stokes back in fourth place.
Joe Root, who marked his first Test as England captain with a notable victory, is now ranked as the second-best Test batsman in the world, after leapfrogging his New Zealand opposite number Kane Williamson in second place thanks to his first-innings 190.
Root had entered the Lord's Test trailing Williamson by 32 points, but now leads him by eight points. Australia's captain, Steve Smith, remains 53 points clear in top spot, on 941 points - the fifth-highest ranking ever recorded.
England's wicketkeeper, Jonny Bairstow, entered the top ten for the first time after his fighting fifty in England's second innings at Lord's, while Alastair Cook, the former captain, rose two places to 11th with his 69. Moeen is England's fourth-highest ranked batsman, in 21st place.
In the bowling table, Moeen's ten wickets mean he has climbed nine places to enter the top 20 for the first time, while South Africa's Vernon Philander and Morne Morkel gained one place each to sit 10th and 13th respectively. The table is headed by Jadeja, with his India team-mate Ravichandran Ashwin second and Rangana Herath of Sri Lanka third.