Despite spurning some gilt-edged chances either side of the interval at Wembley, Kane found his scoring form in the 54th minute when he headed home from Ben Davies' cross, before he brought up his half-century 12 minutes later.
It is a remarkable feat for Kane, who has made a total of 48 appearances for club and country so far this calendar year, playing 4044 minutes and attempting 228 shots.
Kane started the year off in style with a brace in Tottenham's 4-1 victory at Watford on New Years' Day, going on to net a further three Premier League hat-tricks - as well as a four-goal haul against Leicester City - in the back half of 2016-17.
And despite a difficult start to the current campaign, four league doubles, against Everton, West Ham, Huddersfield Town and Liverpool respectively, set him on his way, while the 24-year-old also has a further six Champions League goals to his name and seven goals for Gareth Southgate's England.
The achievement bookends a successful week for Kane, who finished an impressive 10th in Thursday's Ballon d'Or rankings.