Cuthbert stunner keeps Chelsea in touch with Lyon in Champions League
Cuthbert rocketed home a long-distance volley 18 minutes from the end in a stirring second-half display that will give Emma Hayes' side hope of seeing off the French side in England next weekend.
"I think we were better today than Lyon and we showed courage and conviction," said Hayes.
"I feel we deserved the goal we scored, I was happy with that but we should have scored a second and that's why I'm disappointed with the result. The away goal makes the second leg very interesting, it will be hard for Lyon at our place."
Lyon, who are five-times winners of the competition and have won it three years in a row, looked set to cruise through at half-time thanks a deflected Delphine Cascarino strike and a glancing finish from Amandine Henry.
Chelsea squeezed past Paris Saint-Germain 3-2 thanks to a last gasp winner from Maren Mjelde in the previous round, and will be more confident of knocking out the dominant force in women's football after taking the game to Lyon in the second period.
However, they could rue Fran Kirkby missing a generously awarded penalty on the stroke of half-time, and giving away two sloppy goals in the first half that could yet see them knocked out.
"We lost the midfield battle after half-time," said Lyon coach Reynald Pedros.
"We sat back instead of attacking, we made a lot of mistakes with our passing and we were stretched as a team."
Lyon were gifted their opener in the 27th minute when Blues centre-back Magdalena Ericsson turned Cascarino's shot past her own goalkeeper Ann-Katrin Berger.
Chelsea were sloppy again for Lyon's second, giving away an unnecessary corner and then watching the ball sail past everyone via the slightest of touches from Henry.
The London side dusted themselves off after the break and scored a deserved goal thanks to Cuthbert, who met Bethany England's knock down perfectly with a left-footed strike that crashed past Sarah Bouhaddi in the Lyon goal.
The winner of the tie will likely take on Barcelona, who won 1-0 at Bayern Munich thanks to Kheira Hamraoui's 63rd-minutes strike in the other semi-final on Sunday.