Mauricio Pochettino’s went into the game looking to avenge their 4-2 Premier League derby drubbing at the hands of the Gunners just 17 days ago.
And, after Son Heung-min Son put them ahead midway through the first half, it was left to Dele Alli to seal only Spurs' second win at the Emirates Stadium, with a superb finish just before the hour mark.
While it is an early Christmas gift for the Spurs fans, the Gunners supporters have now seen their team lose two games in succession having enjoyed a 22-match unbeaten run until last weekend.
Unai Emery made four changes to the Arsenal starting XI which lost 3-2 at Southampton in the Premier League on Sunday with goalkeeper Petr Cech replacing Bernd Leno, while Ainsley Maitland-Niles, Sokratis and Aaron Ramsey replaced defenders Laurent Koscielny, Hector Bellerin and Stephan Lichtsteiner.
There were also four changes to the Tottenham side which recorded a narrow 1-0 win over Burnley in their Premier League match on Saturday with Harry Winks, Christian Eriksen, Paulo Gazzaniga and Son coming in for Harry Kane, Erik Lamela, Hugo Lloris and Oliver Skipp.
Arsenal started brightly in a lively opening spell with Ramsey having the first serious attempt in the eighth minute as he picked up the ball from Alex Iwobi and flashed a shot just wide of the far post.
Henrikh Mkhitaryan should have put the Gunners ahead in the 12th minute when he exchanged passes with Ramsey before going clear inside the Spurs area, only to hit his shot too close to Gazzaniga who parried it away to safety.
Spurs reacted to that escape and Eriksen hit a rising effort over the top from 25 yards in the 16th minute.
The visitors silenced the Emirates in the 20th minute when a long kick upfield from Gazzaniga dropped to Alli and he sent a lovely ball into the path of Son who advanced into the area before guiding his shot past the advancing Cech.
Pierre-Emerick Aubameyang, who scored twice in the win against Spurs earlier this month, had his first opportunity after being teed up by Matteo Guendouzi down the left on 27 minutes, but he fired low and hard just beyond the far corner of the net.
Spurs should have doubled their lead on the half-hour when they broke from an Arsenal corner and Eriksen teed up Moussa Sissoko on the edge of the box, but he blasted his effort over the top when he should have at least hit the target.
Despite Spurs dominating possession, Arsenal finished the half strongly and they were inches away from going in level at the break when Iwobi crossed from the left to Ramsey who saw his effort from 12 yards tipped on to the post by Gazzaniga.
Sokratis then managed to guide a header wide from a Lucas Torreira cross having done well to outjump the Spurs defence at the back post.
Arsenal came out of the blocks quickly in the second half, but after failing to generate any clear openings, it was Spurs who grabbed the second goal of the evening on 59 minutes.
Substitute Kane had been on the pitch for less than a minute when he picked up possession and quickly picked out the run of Alli in behind the Arsenal defence, and the midfielder then coolly chipped his effort over the stranded Cech with the outside of his right foot from just inside the area.
Arsenal almost responded immediately when Aubameyang came in from the left and his low cross fell to substitute Alexandre Lacazette who watched his first-time effort from six yards hit off the far post before rolling out of play.
The hosts hit the woodwork again on 76 minutes when Aubameyang’s attempted cross from the left almost caught out Gazzaniga as it bounced off the crossbar and away on the far side.