Mikel Merino's first-half header settled the London derby on Sunday and saw second-placed Arsenal move within 12 points of leaders Liverpool.
But in another all-London clash, there was more disappointment for Spurs boss Ange Postecoglou as he watched his side succumb 2-0 at Fulham.
Arsenal's title hopes have faded in recent weeks, but they closed the gap on Liverpool, who were playing Newcastle in the League Cup final later in the day.
Merino rose in the 20th minute to flick Martin Odegaard's near-post corner beyond Chelsea goalkeeper Robert Sanchez, and it proved enough to secure a first league win for Mikel Arteta's team since February 15.
Defeat for fourth-placed Chelsea means they missed the chance to extend their one-point lead over Manchester City in fifth and boost their chances of qualifying for the Champions League next season.
Arsenal, on 58 points, are 10 points clear of four-time defending champions City.
Another setback for Tottenham is likely to only increase the pressure on Postecoglou heading into the international break.
Spurs, in 14th, have only won one of their last five in all competitions, and this was a 15th league defeat of the season.
Rodrigo Muniz gave Fulham the lead in the 78th at Craven Cottage and Ryan Sessegnon doubled the home team's lead 10 minutes later.
Fulham are eighth, four points behind Chelsea in the race for a Champions League place.
