Jermaine Grandison’s own-goal broke Shrewsbury’s hearts after Chelsea survived a scare to snatch a late win.
The Town defender turned in substitute Willian’s cross with nine minutes left but Jose Mourinho’s side were made to work to reach the Capital One Cup quarter-final.
Andy Mangan had scored 84 seconds after coming on as a 75th-minute replacement to cancel out Didier Drogba’s opener before Grandison’s unfortunate intervention.
After the match, Drogba was quick to praise the performance Shrewsbury.
“Fantastic team, fantastic opponent,” the Ivorian said of Micky Mellon’s side.
“I think they give everything. They made it a very difficult game for us.”
Chelsea manager Jose Mourinho insisted he always knew his side was going to be in for a tough game.
“It was difficult from minute one to the last minute. I was worried about the possibility of going to extra-time.”
The Shrews refused to be overawed early on with Nathaniel Knight-Percival forcing a smart early save out of Petr Cech.
Bobby Grant drove over and Collins headed wide as the hosts enthusiasm worried Chelsea.
Aside from two weak Andre Schurrle efforts, they contained their visitors and when Chelsea did threaten Schurrle let them off the hook on 32 minutes.
From Drogba’s excellent pass Mo Salah burst into the area and crossed for the unmarked German who had just Jayson Leutwiler to beat. But, bafflingly, he opted for a cushioned header across the area instead shooting. Salah’s wild strike then flew out for a throw to underline Chelsea’s frustration.
When they did find the net, three minutes before the break, Drogba was offside after steering the ball past Leutwiler following Oscar’s mis-hit.
However, within three minutes of the restart Chelsea were ahead.
Schurrle and Salah combined well to tee up Drogba who clinically steered past Leutwiler from 12 yards.
Shrewsbury almost levelled eight minutes later. Former Republic of Ireland international Liam Lawrence’s free-kick was knocked down to Goldson and his shot deflected off Collins to fly wide with Cech helpless.
Collins and Drogba traded efforts from distance but Town began to run out of steam.
Yet the hosts did equalise with 13 minutes remaining when substitute Mangan, on for Collins, fired in from close range after Chelsea failed to clear Lawrence’s corner.
But they were level for just four minutes when Grandison turned Willian’s low cross into his own net.
SHREWSBURY: Leutwiler, Goldson, Grandison, Knight-Percival, Grimmer, Grant (Clark 67), Woods, Lawrence, Demetriou, Collins (Mangan 75), Akpa Akpro.
CHELSEA: Cech, Christensen, Zouma, Cahill, Luis, Mikel (Matic 80), Ake, Salah (Willian 80), Oscar (Hazard 90), Schurrle, Drogba.
Referee: Neil Swarbrick.