Rakitic stole the spotlight midway through the first half when the Croatia midfielder struck with a thunderous half-volley.
And in their last game, the Catalan giants were held 1-1 by Athletic Bilbao at Camp Nou in which Lionel Messi only came on in the second half and was unable to net the winning goal.
Tottenham are in danger of crashing out at the group stage for the second time in three years.
However, while those moments encapsulated Messi's individual brilliance, his ruthless streak was showcased shortly afterward when, with the score 2-1, he finished off a move of beauty to restore Barcelona's two-goal advantage. What Messi had in skill, Kane matched in grit.
Personal honours have been a hot topic this season, with Messi and former Real Madrid star Cristiano Ronaldo having dominated the Ballon d'Or over the last decade, but challengers like Modric making a strong case to win more awards in 2018.
At the other end Kane tried his best without his usual support acts of Dele Alli and Christian Eriksen (both injured) and he did an admirable job.
However, Tottenham are missing a number of key first-team players through injury and so will not be able to field a full-strength lineup against the winless Bluebirds.
Once again the creation and execution were breath-taking.
Messi put matters to rest just before full-time after a bad giveaway from the Tottenham defence left the Barca talisman alone with only Lloris to beat and he made no mistake, tucking the ball into the bottom right corner to seal the points.
Messi scored twice and hit the post twice in Barca's 4-2 victory at Wembley, but Pochettino insisted the second-minute error of Lloris was more decisive than the brilliant Argentine.
Whether the Spurs players enjoyed it, as Pochettino told them to, remains to be seen, but perhaps in time they will tell their grandchildren about the night they shared a football pitch with Messi.