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.
'It's never easy to play as a visitor in the Champions League and less against a team like Tottenham. "If you watch the first half again, how many chances did he have?"
Croatia midfielder Ivan Rakitic then doubled the lead by firing home an acrobatic half-volley off the inside of the post from 20 yards. Spurs could not get near him and he left the watching crowd gasping twice within the space of five minutes as two nearly identical efforts struck the same portion of Lloris's right-hand post.
The former England star claimed Messi's decision making is better than anyone else now playing.
Asked if she was nervous to be around so many world-class players, she said: "I wasn't nervous but I knew Harry Kane and Lionel Messi were right behind me".
Some more poor play from Lloris saw Messi nearly score soon after as the La Liga giants pushed for a fourth goal. Suarez looked set to hit it at the near post, but instead produced a ideal dummy that left Messi to guide the ball into the corner of the net from six yards.
Ernesto Valverde's men had failed to win their last three games and looked nervy in the closing stages, but Messi capitalised on poor defending in the last minute to ensure his team join Inter on maximum points after two games in Group B. He has five goals in two UCL games this season, at a rate of one goal every 36 minutes.
His longstanding rival Ronaldo has scored 105 of his 120 Champions League goals in the colours of Real Madrid - a record now matched by Messi.
Kane did his job, as he usually does, in holding the ball up and trying to bring others into play, but when he dropped deeper to lay balls off, neither Eriksen or Alli were there to link up with him.