After just over half an hour the sides had managed two shots each. Chelsea then broke out, won a corner in the 31st minute, and floated it toward goal. The ball looked to be curling in before Shaw got the top of her head to it and sent it wide.
Elsewhere, Manchester United beat Crystal Palace 2-0. Elisabeth Terland's finish had put United 2-0 up by the 38th minute, and the result was confirmed as this match reached 54 minutes.
The goal arrived after Chelsea outshot City 4-0 in the final 15 minutes of the first half, according to a live account of the match. They had sat deep, worked a couple of half-chances, and finally took one.
No scorer was identified in the available account, and the live notes did not settle a final score. What they did show was a tight game that opened in City's favour and swung toward Chelsea before the interval.
The teams came out to Liquidator. Both sides defended man to man, a setup that left little room unless a player could escape her marker.
City had the better of the opening 10 minutes. In the second minute, Buchanan held the ball longer than she needed inside her own penalty area. Shaw sensed a chance to steal it, but Buchanan toe-poked the ball to a teammate in time.
Chelsea's Lexi Potter was booked in the 14th minute for a foul on Coffey. A minute later a pass sent Carpenter clear down the Chelsea right. She reached the edge of the area with three teammates offering options, then scuffed a weak shot wide.
Chelsea had a spell on the ball around the 18th minute, a change from that visitor-led start. In the 26th minute McCabe gave the ball away, and quick passes left Wamser a shot from about 25 yards. She could not keep it on target.
Malard went down in the 35th minute and was treated by Chelsea's physios. Lauren Hemp, feeling the right side of her neck, looked able to continue by the 43rd minute.
There was little urgency at the other end of the half. A full two minutes passed in stoppage time between Shaw giving away a free kick and Chelsea taking it.
The second half brought a booking rather than an immediate goal. In the 47th minute Shaw jumped into Bronze instead of contesting the header, then landed on her. The referee showed Shaw a yellow card.
Shaw was involved again in the 66th minute, running into the left side of the penalty area. Forced to check back onto her right foot, she got a shot away that was blocked.
When the players returned to the pitch, Chelsea appeared to be making a third substitution. The notes did not name the player coming on or the player coming off.