The England international had been widely expected to be left out on Sunday, but he captained the hosts from the start and scored a pair of quickfire second-half goals, which eased Spurs' passage into the fourth round.
Wimbledon at Wembley conjures memories of the 'Crazy Gang' and their famous Cup win of 1988 and Jimmy Abdou struck the crossbar in a goalless first half to suggest the improbable may be on the cards once again.
But Kane's double – scored in the space of 111 seconds – and Jan Vertonghen's first Spurs goal since October 2013 saw off the League One side and helped Pochettino avoid the kind of headaches brought on by last season's 4-3 epic in this competition against Wycombe Wanderers.
Pochettino took Spurs to the semi-finals of this competition last term and, with the Premier League seemingly beyond them, he may hope to go even better this time around.
But the sluggish nature of the Spurs support cast's performance in this contest may give him cause to seek January reinforcements.
Kane being paired with Fernando Llorente in attack left the hosts with the more rudimentary looking approach and they struggled to break down Wimbledon's stubborn resistance, despite hogging more than 90 per cent of possession in the opening 15 minutes.
The Spurs captain was crowded out and Erik Lamela was denied by George Long after good set-up play from Llorente, but Spurs were sloppy and Wimbledon went closest to a first-half goal when they finally came out of their shell.
A string of corners gave the Dons confidence and Abdou forced Michel Vorm into an excellent save, curling at the top corner from 20 yards after Lyle Taylor's lay-off, only for the Dutchman to paw the ball onto the crossbar and hold Liam Trotter's follow-up.
It stung Spurs into some renewed vigour, but Long parried Kane's long-range effort clear and got enough on Lamela's deft one-on-one attempt to preserve his clean sheet at the break.
Jonathan Meades' looping header had to be tipped over by Vorm, but Spurs began to click through the gears and Mousa Dembele smashed the post – Long lucky to see the ball not rebound in off him – and Son Heung-min was inches away from converting Eric Lamela's cross shortly after replacing Llorente.
Spurs were energised and finally took the lead in the 63rd minute, Kieran Trippier feeding the onrushing Moussa Sissoko in the right channel and Kane gleefully converting the Frenchman's cut-back.
Less than two minutes later, Kane had a second, sweeping home after Kyle Walker-Peters' shot deflected into his path.
And a seven-minute spell of destruction was completed when Taylor was caught in possession and Vertonghen blasted into the top corner from 30 yards via a deflection off Dons skipper Barry Fuller.
1536 - Jan Vertonghen has scored his first competitive goal for Tottenham in 1536 days, since scoring against Sheriff Tiraspol in October 2013. Wait.— OptaJoe (@OptaJoe) January 7, 2018
Dele Alli, of MK Dons stock, came on to give the away fans something to shout about, gripes that will likely be revisited when they head to stadium:MK next weekend.
Son had a shot deflected onto the post and Georges-Kevin N'Koudou ought to have had a late penalty, but Spurs will have been thankful to avoid any slip-ups, having made clear their determination to add silverware to match their lofty reputation.