The England international found the target on six occasions for Spurs, with that haul achieved in just four outings.
Swansea were the only side to keep him out, as Kane made history by becoming the first man to net two or more goals in three successive away games.
The 24-year-old opened the calendar month with a brace against Everton, before going on to match that achievement at West Ham and Huddersfield.
Kane had made his customary slow start to the season, with his August hoodoo continuing in 2017-18.
He was, however, to break his duck in the colours of England on September 1 and has not looked back.
His efforts against Dortmund remain his only club goals at Wembley so far this season, with Kane yet to trouble the scorers in a Premier League game at Tottenham’s temporary home.
He will get another opportunity to end that barren run on Saturday when Bournemouth pay a visit to north London.
For now, though, Kane can revel in the fact that he is considered to be the pick of the English top-flight performers.
He had faced competition for the September prize from the likes of Manchester City duo Sergio Aguero and Kevin De Bruyne and fellow frontmen Romelu Lukaku and Alvaro Morata.
Seeing off such rivals helps to highlight just how impressive Kane has been of late, with his fine run of form having continued through the recent international break as he netted in back-to-back outings for England.