Burnley were dominant in the first half at Turf Moor, taking the lead through Chris Wood, but a much-improved Spurs battled back after the break to avoid a damaging third straight defeat.
Dele Alli, who scored his sixth goal in five games against Chelsea, praised Tottenham manager Mauricio Pochettino for his approach.
Dele Alli joined Tottenham Hotspur in 2015 and has scored 48 goals in 153 competitive appearances for the club.
Mauricio Pochettino's side are the first club in the Premier League era not to make a single signing since the introduction of the pre-season transfer window.
Almost 20 million people in Britain watched England reach the World Cup semi-finals on television, viewing figures showed Sunday, not accounting for the many more who watched in pubs.
Goals from Harry Maguire and Dele Alli and a string of fine second-half saves from goalkeeper Jordan Pickford were enough for England to progress to the last four.
FIFA World Cup 2018, Highlights, Tunisia vs England: Captain Harry Kane struck in the stoppage time to help England beat Tunisia 2-1
Nothing less than winning the World Cup in Russia next month will be satisfactory despite England's failure to even progress to the later stages in recent tournaments, insist Three Lions' stars Raheem Sterling and Dele Alli.
Tottenham Hotspur edged closer to a third consecutive season in the Champions League by opening up a five-point lead on fifth-placed Chelsea.
Goals from Alexis Sanchez and Ander Herrera cancelled out Dele Alli's opener and ensured that Tottenham's decade-long wait for a trophy continues.
Christan Eriksen's wonder strike levelled in first-half stoppage time, before Alli took centre stage to end a barren run by his standards with two smart finishes just after the hour mark.
Raheem Sterling scored the fastest goal of the Premier League season as leaders Manchester City got back on track with a 3-1 win against Watford on Tuesday
Harry Kane took his goal tally in the Premier League to 36 for the calendar year, equalling the record set by Alan Shearer with Blackburn Rovers in 1995.
Tottenham Hotspur are through to the Champions League last 16 from Group H with two games to spare, while Real Madrid will have to wait to join them.
Pictures and video footage of Alli's gesture were widely shared on social media.
Dele Alli and Harry Kane kept Tottenham Hotspur in the Premier League title hunt as their side torpedoed Arsenal 2-0 while Chelsea maintained their advantage by winning 3-0 at Everton earlier in the day.
Chelsea were bidding to become the first team to win 14 successive games within the same English top-flight season, but Dele Alli's goals, both set up by Christian Eriksen, brought them down to earth.
Tottenham Hotspur beat Watford 4-1 to send them above Manchester City on goal difference and into the top four of the Premier League