Leicester boss Amandine Miquel said this week she hoped to "spice things up" and "surprise" Chelsea at King Power Stadium and they certainly did midway through the first half.
Goalscorer Goodwin was only on the pitch after an early injury to Deanne Rose forced her off within seven minutes - but Leicester responded well to her loss.
They limited Chelsea's chances and frustrated the visitors, proving particularly threatening down the left through Hannah Cain.
Midfielders Yuka Momiki and Ruby Mace pulled the strings and Chelsea were limited to long-range efforts.
The hosts' efforts were acknowledged by supporters at the break, while Chelsea's players trudged down the tunnel - manager Bompastor struggling to hide her emotions as she waved her arms in the air in dismay throughout the opening half.
This was a situation her side had not faced this season and Bompastor did not waste time making changes, continuously adding strength off the bench as they chased an equaliser.
Leicester centre-back Sophie Howard continued to put in an impressive individual display but the hosts were clinging on.
The drums grew louder from the home supporters' end as they urged their team on, while Bompastor ran down the touchline on occasions to collect the ball, keen to maintain Chelsea's intensity.
After Kaptein pulled them level, the chance they had been looking for to win the game came deep in stoppage time when Sjoeke Nusken was teed up by Mayra Ramirez in the box, but she sent the ball sailing over the bar, sparking groans from the away end and huge celebrations from Leicester fans.
When the whistle went for full-time, Leicester's players jumped up in celebration and gathered in a huddle inside their box, while the Chelsea players fell to their knees in disappointment.
"You could see the body language. Everyone is frustrated. We all have the same ambitions," said Chelsea boss Bompastor.
"It will be good now to see how we react from that. We will stay together no matter what as that's really important."
It opens the door for Chelsea's title rivals Manchester City, who can close the gap to three points if they beat Everton on Sunday.