Trott climbs above Indian Sachin Tendulkar and Kumar Sangakkara after scoring 70 and 22, but remains behind South African Jacques Kallis.
Anderson moves ahead of compatriot Graeme Swann, who is the world's best one-day bowler, after a five-wicket haul in the second innings.
Chris Tremlett rises to a career-high ninth and becomes the third Englishman in the top 10 after taking four wickets.
Another South African, Dale Steyn, tops the bowling rankings.
England's 196-run victory on Monday put them 1-0 ahead in the four-match test series against the world's number one Test side, whom England hope to displace at the end of the series.