Jurrien Timber's second-half goal ensured Arsenal re-established a five-point lead over second-placed Manchester City on Sunday, the day after Pep Guardiola's team had kept the pressure on by beating Leeds.
Overcoming a major rival with the Chelsea win, they're a step closer to a first league title since 2004.
They visit City next month in what shapes as the key hurdle for Mikel Arteta's team, who have no other games against the rest of the current top seven in the standings.
"We have the feeling we have to win and win and win. You win so many games, but it is not enough to open the gap. That is the level of this league," Arteta said.
This felt like a key day in the race as, even down to 10 men, Chelsea pushed deep into added time for an equaliser.
David Raya produced a stunning save to push Alejandro Garnacho's goalbound cross away as the seconds ran down at the Emirates, and Liam Delap's goal for Chelsea was ruled out for offside in the dying moments.
William Saliba had put Arsenal in front, converting from a corner after 21 minutes and though Piero Hincapie's own-goal got Chelsea back into the game in first-half added time, Timber headed in from another corner in the 66th.
Benjamin Sesko's seventh goal in eight games sealed victory for Man Utd against Palace, moving them above Aston Villa on goal difference. "It feels like a big result," United captain Bruno Fernandes said.
It further strengthened interim boss Michael Carrick's credentials to be given the coach's job full-time as he took his unbeaten record to six wins in seven games.
Over two spells as United coach, Carrick has now picked up 23 points from nine games -- the joint-highest points total in the league's history for any manager after his first nine games, equalling Ange Postecoglou's start at Tottenham.
Maxence Lacroix headed Palace in front after just four minutes, but United equalised in the 57th minute after Lacroix dragged back Matheus Cunha in the box and was sent off.
Bruno Fernandes converted his seventh goal of the season from the penalty spot and Sesko struck again with a powerful header in the 65th.
At the other end of the standings, Tottenham's winless run extended to 10 games after a 2-1 loss at Fulham — leaving them mired in a fight to avoid relegation. Nottingham Forest are also in trouble after a 2-1 loss at Brighton.
Tottenham are still without a league win in 2026 after new coach Igor Tudor made it back-to-back losses in his first two games in charge. It's equalled their longest winless streak in the Premier League, matching a record that dates back to 1994.
First-half goals from Harry Wilson and Alex Iwobi gave Fulham a 2-0 lead at the break, Richarlison pulling one back in the second half.
Tottenham are 16th, four points and two places above the relegation zone with 10 rounds to go, while Forest are 17th and two points clear after two-straight losses in the league.
