Broad finished the third Test between England and West Indies with a match haul of 10 for 67 during which he touched the milestone of 500 Test wickets.
However, with Broad moving seven places to break in to the top 10, India's Jasprit Bumrah was pushed down a spot to be placed eighth in the bowlers list.
Sachin, who had earlier backed Broad to come good in the second Test, said that the right-handed bowler was out on a mission and congratulated the England side for their "emphatic series win".
The 34-year-old Broad is only the seventh bowler in history to have taken 500 Test wickets and the fourth quick.
Broad becomes the second Englishman to achieve this impressive feat after partner-in-crime James Anderson.
Broad's haul of 6-31 in 14 overs saw the West Indies bundled out for 197 in reply to England's first-innings 369 that featured his dashing 62.
Broad was dropped for the first test — won by the West Indies in Southampton — and didn't take it well, expressing his disappointment in a TV interview.
Warne had tormented England with the ball for 14 years and holds the record for the most Test runs without a century.
England's slump against a new ball well deployed by Kemar Roach and Shannon Gabriel started when Ollie Pope failed to add to his overnight 91.
England lead by 219 runs and Broad feels if they can score quick runs in the first session then they are capable of forcing a result in the final two sessions of the day.
Broad last missed a home Test when he was rested against West Indies in 2012 and with 485 Test scalps is only second to Anderson in terms of highest wicket-takers for England.
Create a mindset to help us perform in absence of crowds: Stuart Broad tells England sports psychologist
The upcoming three-match Test series between England and West Indies, starting here on July 8, will mark the resumption of international cricket after the coronavirus-forced hiatus.
The coronavirus outbreak has caused a collapse of sports events worldwide, forcing either cancellations or postponements.
South Africa were 215 for eight the close, still 54 runs behind England's first innings total of 269 on a dry pitch which is likely to get more difficult for batsmen later in the match.
Television footage has shown Australian fielder Cameron Bancroft taking an object out of his pocket and appearing to rub it on the ball in the third Test in Cape Town on Saturday.