The striker hit the 30 mark in all competitions and 20 in the Premier League with the third goal in our 3-1 win at Newcastle on Sunday.
In doing so, he became just the 10th player since we joined the Football League in 1908-09 to hit 30 goals in all competitions in a season.
Bert Bliss was first to achieve it back in 1919-20 with 33 goals and it's been done another 19 times by another nine players now, including Harry.
Not surprisingly, all-time great Jimmy Greaves leads the way by hitting 30 goals on six occasions, part of his record 266 goals for us in 379 appearance.
Bobby Smith also managed it four years on the trot and the double-winner is second on our all-time list behind Greavsie with 208 goals in 317 appearances.
Martin Chivers - our all-time record goalscorer the League Cup and until recently in Europe (until he was taken over by Jermain Defoe) - is third in our all-time list and topped the 30 mark twice in 1971-72 and 1972-73.
More recently, Clive Allen scored a club record 49 goals in 1986-87 while Gary Lineker was the last Spur to hit 30 before Harry with 35 in 1991-92.
Here is our 30-plus club...
BERT BLISS (104 goals in 215 appearances, 1912-1920)
33 goals in 46 appearances, 1919-20
Signed from Willenhall in 1912, Bliss top-scored as the club was relegated in 1914-15 but after the First World War, he top-scored again with 31 as we gained promotion back to the top flight. He also scored twice in the semi-final against Preston as we won the FA Cup in 1921.
TED HARPER (63 goals in 67 appearances, 1929-31)
37 goals in 32 appearances, 1930-31
Signed from Sheffield Wednesday in 1929, Harper set a then-club record 36 league goals in 1930-31 - a total that came despite an injury that forced him out of six of our last eight games. He moved to Preston in 1931 and top-scored for North End - the third time he'd done that at three different clubs.
GEORGE HUNT (138 goals in 198 appearances, 1930-37)
36 goals in 43 appearances, 1932-33
35 goals in 43 appearances, 1933-34
Known as the 'Chesterfield Tough', England international Hunt signed from Chesterfield in 1929 and took over when Ted Harper was injured at the end of the 1930-31 campaign. He kept his place and led the team to promotion in 1933.
JOHN MORRISON (101 goals in 154 appearances, 1933-39)
35 goals in 37 appearances, 1936-37
The third of our trilogy of lethal strikers in the 1930s alongside Ted Harper and George Hunt, Morrison took his chance when Hunt was injured in 1935 and led the goalscoring charts in 1936-37. First-choice at the start of the Second World War, he played just one more game after the conflict in 1945 before retiring.
BOBBY SMITH (208 in 317 appearances, 1955-64)
38 goals in 40 appearances, 1957-58
35 goals in 40 appearances, 1958-59
30 goals in 44 appearances, 1959-60
33 goals in 43 appearances, 1960-61
The classic 'old-fashioned centre-forward', Smith's battering-ram style put fear into defenders and goalkeepers alike. Top-scorer in our famous double-winning team - he opened the scoring in the 1961 FA Cup Final as we made history - Yorkshire-born Smith reeled off 30-plus goals in four-successive seasons. He also scored in the 1962 FA Cup Final and played in the 1963 Cup Winners Cup triumph.
JIMMY GREAVES (266 goals in 379 appearances, 1961-70)
30 goals in 31 appearances, 1961-62
42 goals in 48 appearances, 1962-63
36 goals in 45 appearances, 1963-64
35 goals in 45 appearances, 1964-65
31 goals in 42 appearances, 1966-67
36 goals in 52 appearances, 1968-69
The greatest goalscorer of his and perhaps any era, Greavsie is our all-time record marksman and hit 30-plus in six of his nine seasons at Spurs. Snapped up by Bill Nicholson from AC Milan in December, 1961, he joined the double-winning squad and weighed in with 30 goals despite not making his debut until December 16! He scored in the 1962 FA Cup Final, the 1963 Cup Winners Cup Final and added another FA Cup in 1967. He remains fourth in England's all-time list as well with 44 goals in 57 caps.
MARTIN CHIVERS (174 goals in 367 appearances, 1968-76)
42 goals in 62 appearances, 1971-72
33 goals in 65 appearances, 1972-73
Spearhead of Bill Nicholson's trophy-winning team of the early 1970s, 'Big Chiv' joined us from Southampton in 1968 and stands third in our all-time goalscoring list. He scored twice to land the League Cup in 1971 and twice again as we lifted the UEFA Cup against Wolves in 1972. He cracked 30-plus goals twice and 29 in 1970-71.
CLIVE ALLEN (84 goals in 135 appearances, 1984-88)
49 goals in 54 appearances, 1986-87
Son of double-winner Les Allen, Clive holds the record for most goals in a season after his staggering campaign in 1986-87. Deadly in David Pleat's 4-5-1 system, he scored 33 goals as we finished third in the league and another 16 as we reached the FA Cup Final - he scored in the loss against Coventry at Wembley - and semi-final of the League Cup. He was named PFA Player of the Season and Football Writers' Association Footballer of the Year for his efforts.
GARY LINEKER (80 goals in 138 appearances, 1989-92)
35 goals in 50 appearances, 1991-92
Lethal around the box, Lineker joined us from Barcelona in 1989 and went on to star alongside team-mate Paul Gascoigne at the 1990 World Cup. He returned to lead us to the FA Cup Final in 1991 with a double in our famous semi-final win against Arsenal at Wembley and then struck 35 goals in the 1991-92 campaign before departing for a new challenge at Grampus Eight in Japan. He remains second in England's all-time list with 48 goals in 80 caps.
HARRY KANE (35 goals in 72 appearances, 2011-present)
30 goals in 46 appearances, 2014-15
Young striker who burst onto the scene with three-successive goals in the Premier League last season. His goalscoring exploits in the Europa League earned a starting place in the PL in November and he hasn't looked back in a stunning 2014-15 campaign so far where he's scored his first Spurs hat-trick, his first PL hat-trick, become the first home-grown player in 30 years to hit 20 league goals and the first player since Lineker to hit 30. On top of that, he scored just 79 seconds into his full England debut against Lithuania at Wembley in March!