The 24-year-old Yorkshireman struck a superb 130, his second hundred of the series, in England's innings and 78-run win in the fourth Test at Trent Bridge on Saturday.
Victory, completed inside three days, gave England an unbeatable 3-1 lead in the five-match series.
Root has scored 443 runs in the series, with two hundreds and two half-centuries, at an average of 71.79.
The latest edition of the International Cricket Council's rankings published Sunday saw Root on top of the batting standings, with Australia's Smith, out for six and five in Nottingham, dropping down to third place.
Meanwhile the equivalent bowling rankings saw England's Stuart Broad climb to a career-high second place on the back of a stunning first-innings return of eight for 15 on his Nottinghamshire ground that was behind Australia's collapse to 60 all out.
The 29-year-old pacemen's ninth wicket of the match, taken in the second innings, saw him edge past fast bowling great Fred Trueman into fourth place in England's list of all-time leading Test wicket-takers.
Broad has taken 308 wickets in 83 Tests to date and is 17 behind former England fast bowler Bob Willis.
Australia fast bowler Michell Johnson moved down two places to seventh.
Victory at Trent Bridge also produced a statistical landmark for Alastair Cook as he became only the third English captain, after W.G. Grace and Mike Brearley, to twice win the Ashes on home soil.
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