Broad, the man Australian supporters love to hate after he notoriously refused to walk after an umpiring howler during the 2013 Ashes series, took six wickets for 17 runs in a devastating burst as England bowled the hosts out for 83 in their second innings.
England then knocked off the victory target of 74 easily.
Broad, 29, moved above Ravichandran Ashwin of India and South Africa’s Dale Steyn into top spot – the first time an English bowler has topped the ICC rankings since Steve Harmison in 2004.
Australian captain Steve Smith leads the batting rankings, although Joe Root moves up to second after his century for England.
South Africa will lose their top-ranked status to India following the fourth test against England. They trail 2-0.
Australia is poised to usurp the throne if it wins its tour of New Zealand next month.
Meanwhile, NZ openers Martin Guptill and Kane Williamson eclipsed the Twenty20 partnership world record as they bounced back to hammer Pakistan by 10 wickets in their second T20 in Hamilton.
The in-form duo steered the Black Caps to 0-171 off 17.4 overs with little bother, to overhaul the tourists’ 7-168 and square the three-match series 1-1.
The decider is in Wellington on Friday.
Guptill (87 not out) and Williamson’s (72no) unbroken stand is the best for any nation and for any wicket in the history of T20 internationals.
It passes the 170 shared by South African openers Graeme Smith and Loots Bosman against England at Centurion in 2009.
The pair barely offered a chance as they both cruised past 50 at a crisp rate, with Guptill accelerating once he’d passed the milestone, having played second-fiddle to his skipper until then.
The pair have been in electric form for most of the summer but didn’t fire in the 16-run loss at Auckland on Friday, when Guptill was run out for two while Williamson lacked his usual timing, despite anchoring the unsuccessful chase with 70.
The clean-striking Guptill finished with four sixes and nine fours in a 58-ball stay while Williamson tallied 11 fours during his 48 balls. His innings was notable for the frequency with which he stepped across his stumps to work the ball to the leg-side boundary.
The Pakistan attack which looked so threatening at Eden Park had no answer, with spinners Imad Wasim and Shoaib Malik the only bowlers to boast an economy rate below nine.
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