Arsenal boss Arsene Wenger hailed his players' fantastic spirit after the leaders survived a dramatic late Chelsea rally to stay five points ahead of Manchester United.
Mario Stanic and Emmanuel Petit replied within a minute after quick-fire goals by Giovanni van Bronckhorst and Thierry Henry gave the Gunners a 3-0 advantage.
Arsenal had taken a ninth minute lead when Marcel Desailly put through his own goal under pressure from Dennis Bergkamp.
Wenger said: "It was a great start to the new year for us. We were jaded physically but our fantastic spirit got us through. We had to dig very deep." He added: "I wanted us to keep a clean sheet. Then, at 3-0, we relaxed and we were punished, so the last few minutes were very tense.
"But I'd prefer to look on the positive side of this game, our spirit. The team showed they're not just great players - they're winners." The game burst into life in the last ten minutes after a scrappy contest in rainy conditions.
Bergkamp is still seeking his 100th goal for Arsenal. He turned away in triumph after appearing to finish Ashley Cole's cross but Desailly was later 'credited' with the final touch.
Substitute van Bronckhorst seemed to have wrapped up the points when he ran on to Henry's 81st-minute pass to hit a spectacular 25-yard shot past Chelsea keeper Carlo Cudicini.
Henry added a third a minute later, with a weak effort that slipped through Cudicini's grasp.
But Wenger's team were made to sweat. Stanic headed in ex-Gunner Petit's 85th-minute corner after Jimmy Floyd Hasselbaink nodded the ball back.
A minute later, Petit seized on a mix-up between David Seaman and Sol Campbell to net Chelsea's second. The days when Arsenal's defence was rock-solid have gone.
Chelsea, who made six changes, drop to third, eight points behind the leaders. They have not won a league match at Highbury for 13 years.
They relied heavily on Gianfranco Zola for creative ideas and substitute winger Jesper Gronkjaer wasted several chances to pressure Arsenal with crosses.