The tourists were bowled out for 179 in their second innings with Anderson on 3-30 as he became the leading wicket-taker among pace bowlers across all formats by moving past Australian Glenn McGrath's total of 949 with his second scalp.
They had resumed their second innings on 23 without loss after England's mammoth 415-9 on Friday, but Anderson and fellow seamer Ollie Robinson (4-43) were excellent with their line and length to level the three-match series at 1-1.
The visitors resumed on their overnight 23 without loss and captain Dean Elgar was the first out for 11 when he was bowled by Anderson with a superb delivery that crashed into off-stump.
In doing so, the England seamer became the joint highest wicket-taker among fast bowlers across all formats, drawing level with Australian Glen McGrath on 949 scalps.
Opener Sarel Erwee never looked comfortable at the crease but made his way to 25 before he edged Ollie Robinson to wicketkeeper Ben Foakes.
Aiden Markram's wretched time with the bat continued when he was caught by second slip Zak Crawley off the bowling of Stuart Broad.
Markram scored six having been bowled by Broad off a no-ball in the seamer's previous over. He could not take the life given.
Keegan Petersen and Rassie van der Dussen did their best to halt England but both were dismissed by Ben Stokes just after tea.
Once they had departed, England rolled South Africa's long tail, Robinson and Anderson taking two wickets each with the new ball.
The third test will be at The Oval from September 8th. South Africa won the first match by an innings and 12 runs at Lord's.
