Defender Kieran Trippier scored his first goal for Spurs in the second half to earn them a narrow, but ultimately comfortable, victory as the visitors failed to produce a single shot on target.
Manchester City's loss to title rivals Leicester City earlier in the day had opened up the opportunity for Pochettino's men to climb the table, and they did just that with an impressive performance.
That combination of results adds extra spice to their game with Manuel Pellegrini's side at the Ethiad Stadium next Sunday.
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"I think it is great, the feeling is fantastic," Pochettino said on Sky Sports when asked about jumping into second spot.
"The feeling is better because the performance was fantastic. I feel very proud of my players, the effort was brilliant.
"We need to keep going, always believe we can get better, try to improve and at the end of the season we will see what happens. The reality is we are second but then is the real test for us [against City].
"We need to be calm. We are in a very good position in the league but the philosophy from the beginning of the season has been to go step by step. We are a very young squad so it is important to keep going and take every game and competition and be ready to compete.
"It is very important to recognise the atmosphere at the stadium because our supporters were brilliant at a time when the team needed to feel the patience to try to score. I say 'Thank you', because at a difficult moment of the game when we played well, created a lot of chances, the team needed them."