Both sides struggled to create chances in the early stages but Alli broke the deadlock in first half injury time with the first of two headed goals.
Chelsea’s defence has received plenty of plaudits this season but they were caught napping by the England international, who found space in into the box between Cesar Azpilicueta and Victor Moses all too easily for Christian Eriksen to pick out with an excellent delivery.
Alli’s rose to meet the cross and sent the ball beyond Thibaut Courtois in the Chelsea goal.
The visitors started strongly after the break and Diego Costa forced a good save from Hugo Lloris but they found themselves further behind on 54 minutes.
Again it was Eriksen who provided the ball for Alli’s second, in almost a carbon copy of the Spurs opener.
The Blues pressed but couldn’t find a way through as they failed to become the first side to secure 14 consecutive top flight victories in the same season, while Spurs preserved their unbeaten home record.
Chelsea remain the league leaders and they hold a five point lead over second placed Liverpool, with Spurs now seven points off the pace in third spot.
Everton have joined the race to sign Crystal Palace winger Wilfried Zaha but will face strong competition to land him.
Manchester United are stepping up their interest in Tottenham star Toby Alderweireld and will sell Eric Bailly to fund a deal.