The Blues produced a brilliant first-half performance, finding themselves 4-1 up at the break thanks to a Pedro brace, Giroud's strike and a comical Simon Deli own goal.
But Petr Sevcik scored two fine long-range efforts early in the second period, causing the atmosphere at Stamford Bridge to become extremely tetchy towards the end.
Chelsea ultimately did enough to advance 5-3 on aggregate, but their second-half display will have alarm bells ringing and undoubtedly give semi-final opponents Eintracht Frankfurt reason for optimism.
Through to the last four, where we will play German side Eintracht Frankfurt!— Chelsea FC (@ChelseaFC) April 18, 2019
Bring it on! pic.twitter.com/WLB8v8KJQx
"We started well with good intentions," Giroud told BT Sport. "We have been efficient up front and solid at the back, but we dropped our intensity after the break.
"But this team never gives up and the last 10 minutes was box-to-box. It was a good fight and now we are in the semi-finals."
Not only did Sevcik's brace give Slavia greater encouragement,
"It was a great experience for me," he is quoted as saying by UEFA. "I am a lifelong fan of Chelsea and it was a fulfilled dream for me.
"I was a bit lucky, especially with my right-footed goal. But two goals against Chelsea, it is a dream."