Barca's victory also ended a three-game winless run and Alba praised their performance against Spurs.
Messi almost put the game away twice at the start of the second half, but both times his low curling shots clattered off the left post to keep Spurs trailing by just two goals. And their job at Wembley was made no easier when Hugo Lloris came flying off his line in the second minute to make Philippe Coutinho's life a lot easier as he stroked the ball home from the edge of the box. "But I think for Barcelona it was worse because in the history of football Barcelona always try to play along the grass".
"All Champions League matches are like that".
"As for Messi, what else is there to say?"
'I feel blessed that I was in this stadium live to be able to watch him.
He plays at another level, he scores goals, he provides assists, he runs as much as the most.
Spellbound by Messi's magic, Tottenham backed off again moments later as the striker hit the woodwork for a second time.
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A great start for Barcelona, what Lloris had in mind will remain a mystery.
Nobody disputes the genius he showed for the first time more than a decade ago and has demonstrated consistently since but, after so long at the top and having played more than 800 games, we have to accept that nights like these, when he illuminated Wembley, might be less frequent. As the case was with the 2 goals scored by Kane and Lamela in the second half.
Powering into the Barca area with intent, Kane side-stepped Nelson Semedo and planted a powerful low strike into the far corner for his 10th goal in 12 Champions League appearances.
With two defeats in two, Spurs will now find it hard to qualify as both Barca and Inter Milan already have six points, although Pochettino was adamant it was not over yet.
The hosts were back in the game in the 65th minute, with Erik Lamela's shot from distance taking a deflection off Gerard Pique and sailing past Marc-Andre Ter Stegen.
Barcelona were vulnerable so they said, but on a pitch scarred from hosting British heavyweight champion Anthony Joshua's fight against Alexander Povetkin they took only two minutes to catch Spurs in the solar plexus.
But the damage was done due to defensive errors from Lloris and Sanchez as they badly missed Vertonghen's calming influence and Dembele's presence in front of the back four.