The cagey first half was transformed after the break with two goals in as many minutes from Dele Alli and then Harry Kane from the penalty spot and the Gunner never recovered.
The three points all but confirms Champions League football next season for Spurs, after Chelsea took a huge step towards winning the title by brushing aside Everton with their own second-half blitz.
Another tense opening 45 minutes led to a lively second half as Pedro's stunner from distance settled the visitors' nerves before Gary Cahill and Willian sealed a 3-0 win.
EPL Table | Premier League standings after Gameweek 35
Manchester City were held to a 2-2 draw with Middlesbrough, hampering their top-four chances soon after Manchester United missed the chance to go third as Gylfi Sigurdsson's stunning free kick earned Swansea a point at Old Trafford.
Spurs now host Arsenal in their final north London derby at White Hart Lane knowing a win is a must to keep their title hopes alive having seen Chelsea once again move seven points clear.
On Saturday, Sunderland's relegation was confirmed as they lost 1-0 at home to Bournemouth courtesy of a late Josh King goal.
Jamie Vardy continued his red-hot run in front of goal as Leicester eased their Premier League relegation fears with a 1-0 win at West Brom.
Crystal Palace have enjoyed a stellar April with wins over Chelsea, Arsenal and Liverpool, but fell to a 2-0 home loss to Burnley. The Clarets earning their first away win of the season.
Eldin Jakupovic's penalty save secured what could prove to be a precious point for relegation-threatened Hull as they drew 0-0 at Southampton.