Victor Wanyama's late goal - his first for the club - was enough for Spurs, who dominated for the majority of the game but struggled to find a way past the impressive Wayne Hennessey in the Palace goal.
Pochettino tries new formation, whilst Palace make one change
Spurs boss Mauricio Pochettino implemented a brand new 4-4-2 formation to his side. New signing Vincent Janssen made his full debut, having appeared as a half-time substitute against Everton last week, to partner stand-in captain Harry Kane up top.
To accomodate the change of shape, Dele Alli dropped to the bench. Michel Vorm replaced the injured Hugo Lloris in goal.
Alan Pardew made just one change to the Palace side that disappointingly lost 1-0 at home to West Brom on the opening day. Joe Ledley came in for Mile Jedinak, who is no longer a Palace player having joined Championship side Aston Villa in midweek. Pardew was also able to name new signing James Tomkins on the bench following his return from injury.
Impressive Hennessey keeps Eagles level in first half
Pochettino's attacking line-up showed plenty of promise in the opening stages and the Eagles needed Scott Dann to make two good blocks to deny chances in the opening stages.
Toby Alderweireld then had the first clear-cut chance of the game; powering a header, unchallenged by the Palace defence, straight at Hennessey. The Wales goalkeeper, fresh from his side's heroics at Euro 2016, was called into action almost straight away as he tipped a Kane effort away for a corner.
Janssen had an impressive first start in English football following his move from AZ Alkmaar in the summer. With just under half an hour played, the Spurs number nine found Hennessey at his very best once again, pulling off a superb double save to deny the striker a first competitive goal for his new club.
Palace struggled to get forward in the first half and their lack of presence in the final third has been a worry for their fans for several months. However, the signing of Christian Benteke, announced just hours before kick-off at White Hart Lane, will surely give them a boost.
Benteke was not registered in time to start and, in his place, Connor Wickham had very minimal support and was often outnumbered by the imposing pair of Alderweireld and Jan Vertonghen.
Palace's saving grace, yet again, was their back five, including Hennessey in goal. The Eagles were extremely fortunate to head into half-time still on level terms.
Improved Palace create better chances in second half
Pardew introduced Yohan Cabaye to the action at the start of the second half, replacing Ledley, and Palace's ball retention soon improved.
The Frenchman had an immediately positive effect on his side and he soon exchanged passes with Andros Townsend and Chung-yong Lee before firing wide of goal.
Tottenham responded, though, and went extremely close to taking the lead when Kane tried to direct the ball goalwards following a superb pass from Eric Dier. However, it drifted just wide of goal with Hennessey seemingly beaten.
Townsend, playing for Palace against the Club where he started his career, was much improved in the second half and created another chance for Cabaye, who lashed over the crossbar.
Wanyama strikes late
Spurs appeared to be running out of ideas following their good start to the game, but finally found a route past Hennessey with just eight minutes remaining.
The Lillywhites had a succession of corners throughout the game and eventually one paid off as Kane flicked the ball on to Wanyama, who nodded the ball into the goal.
The goal was certainly no more than Spurs deserved having been the better side for the majority of the game, although Palace will certainly feel hard done by after their improved second half.
The result puts Pochettino's side on four points after two games, whilst Palace are still yet to record a point.