Tottenham took the lead in the third minute of the match when Kane bundled the ball home from close range.
Indeed, a dangerous cross came into the Tottenham box and in an attempt to clear, Cardiff captain Sean Morrison poked the ball against Kane and it rebounded into the bottom corner of the net.
Tottenham doubled their advantage in the 12th minute, however, when Eriksen found space just inside the Cardiff box before picking out the bottom corner with a super finish.
Two then became three in the 26th minute when Son faced up to the challenge of Morrison before firing a low effort into the far corner to all but decide the contest.
Son sent another effort over the Cardiff crossbar 15 minutes before the end of the first period as Tottenham threatened to cause further embarrassment.
Murphy was easily Cardiff's best player in the first period as he caused Kieran Trippier problems down the Tottenham right, but Reid and Callum Paterson were struggling to make the most of the attacker's good work.
Tottenham only had three shots on target in the first 45 minutes, but all three ended up in the back of the net as Pochettino's side took a huge step towards returning to second spot in the table.
Junior Hoilett replaced Murphy at the interval and had a half-chance to register for Cardiff early in the second period when he climbed above Trippier inside the Tottenham box, but Hugo Lloris made the save.
Tottenham did not have the same intensity to their play in the early stages of the second half, with the London outfit seemingly prepared to coast to all three points after doing most of the work in the opening 45 minutes.
Kane struck over the Cardiff crossbar just past the hour mark, before the England captain was twice denied by blocks inside the penalty box as the visitors looked for a fourth.
Cardiff goalkeeper Neil Etheridge then made a smart save to prevent Son from firing home in the 67th minute after Kane had picked out his fellow attacker.
Hoilett and Aron Gunnarsson both brought smart saves from Lloris in the period that followed as Cardiff looked to give their supporters something to cheer on New Year's Day.
Hoilett cut inside before sending one over the crossbar 10 minutes from time, with the attacker impressing after coming off the bench at the break.
There were no goals in the second half of action, however, as Tottenham ran out three-goal winners in Wales courtesy of an excellent first 45 minutes.
Next up for Tottenham is an FA Cup third-round clash with Tranmere Rovers on Friday night, while Cardiff will attempt to return to winning ways when they travel to Gillingham in the FA Cup on Saturday.
CARDIFF CITY (4-3-3): Etheridge; Manga, Morrison, Bamba, Cunningham; Arter, Gunnarsson, Camarasa (Ralls 59'); Murphy (Hoilett 46'), Paterson, Reid (Mendez-Laing 72')
TOTTENHAM HOTSPUR (4-2-3-1): Lloris; Trippier, Alderweireld, Sanchez, Rose; Winks, Sissoko; Eriksen, Alli (Llorente 86'), Son (Skipp 76'); Kane