Pressure was on Arsenal after successive draws against Manchester United and Crystal Palace, meaning they were already playing catch-up in the WSL title race.
With leaders City up next, it could get even worse for the Gunners, who look stuck in a rut and stale in front of goal.
Renee Slegers' side dominated much of the first half without really creating any clear-cut chances - forced into taking shots from distance and shuffling the ball around the box.
They did hit the post twice but both were from tight angles and rarely tested goalkeeper Hannah Hampton in a first half that promised more than it delivered for the visitors.
Arsenal improved in the second half as Slegers made attacking substitutions, but Chelsea stood firm and did their job defensively.
In the end, the Gunners had 19 shots but only two on target - a tally Chelsea tripled despite having less entries in the final third.
There was also worrying confusion from Arsenal's players with their positions at times throughout as Kim Little switched roles in midfield and Alessia Russo dropped back having started as a striker.
When asked about the confusion, Slegers said: "That happened the same time as [Emily Fox] going down and we had to change shape for one minute, then get back into shape after.
"That was the discussion and it maybe looked more than it was as we just had to get the message out as quickly as possible."
It has been the story of Arsenal's season so far - dominating games and having numerous efforts on goal but failing to capitalise, eventually dropping points.
It was chaotic at times from Arsenal, who know their hopes of winning the WSL title could already be hanging in the balance just four weeks into the season.
"Confidence is something that fluctuates. The [players] know who they are and what they can bring," added Slegers.
"There are always phases in the season and different things you need to work on. It's important we keep any pressure away from the players because we believe in them.
"They can be ruthless in front of goal and they can score. It's really important we keep that simplicity and clear minds for the players."