The Magpies were forced into early chances in a goalless first half with Paul Dummett and Florian Lejeune coming off.
The Spurs keeper shipped five goals last time he played at St James' Park - May 15, 2016 - and the 5-1 defeat cost his side second place in the table that season.
Harry Kane leads the line, while Eric Dier - who has previously played at full-back - and Mousa Dembele play in central midfield.
While there hasn't been any signing made, it's believed Everton's Ross Barkley is a very possible summer arrival.
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Pochettino said: "He was calm - that's important".
With the scores locked at 0-0 at the time of the red card, Spurs took full advantage of the numerical superiority and goals from Alli and Ben Davies secured all three points.
Spurs have never lost a game in which Alli has scored, and they made this game secure in the 69th minute when a handsome passing move intitiated by Mousa Dembele, then facilitated by Alli and Kane, ended with Ben Davies stroking the ball into the Newcastle net from close range.
Tottenham manager Mauricio Pochettino has come under pressure to add some new players to a squad that finished second to Chelsea last season and has lost right back Kyle Walker, who moved to Manchester City. They were fantastic last year supporting the team and they will be the same this year.
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