Didier Drogba put the visitors ahead at Greenhous Meadow, but they needed a helping hand from their brave opponents after suffering a scare when Andy Mangan equalised.
Jose Mourinho lifted the League Cup trophy twice in his first spell with Chelsea and named a solid line-up to show he clearly means business once more.
However, the Premier League leaders were made to work hard for their place in the quarter-finals.
Shrewsbury went into the game on the back of four straight League Two wins and had already beaten Premier League side Leicester City and two Championship outfits in this competition.
Their confidence and self-belief was evident in an even first period and the manner of the defeat was ultimately harsh on the home team.
Mourinho made seven changes to the side that started Sunday's 1-1 draw at Manchester United, with 18-year-old Dane Andreas Christensen making his debut at right-back.
Kurt Zouma and Nathan Ake were other youngsters called up, while Petr Cech got the nod in between the posts and Jon Obi Mikel, Mohamed Salah and Andre Schurrle also came in.
Shrewsbury suffered a setback when James Wesolowski went down in the warm-up, meaning a late step up for Liam Lawrence in midfield.
Cech had to be alert in the opening stages as Nathaniel Knight-Percival was on target with a far-post header from a corner and Ake received an early booking for a rash challenge on Bobby Grant.
With the rain driving down, the underdogs had a penalty appeal for handball against Drogba turned down from another set-piece as they more than held their own up to half-time.
Drogba did have the ball in the net at the other end, but a flag was already up for offside and it was a far from comfortable first period for the visitors.
Chelsea started the second half much more positively, though, and Schurrle and Salah combined to set up Drogba, who took full advantage when firing a low volley past Jayson Leutwiler on 48 minutes.
Schurrle then had a 30-yard rocket tipped over the bar, but Shrewsbury did threaten a response when Jean-Louis Akpa Akpro's shot deflected just wide.
Leutwiler did well to keep out a fierce Drogba effort as Chelsea began to dominate proceedings, but the visitors were stunned when Mangan levelled from close range after Grandison headed down a corner.
Hopes of an upset were soon dashed, though, when substitute Willian whipped in a cross from the left wing on 81 minutes and the unfortunate Grandison steered the ball into his own net under pressure from Drogba.
Akpa Akpro did threaten with a late header but there was to be no second reprieve for Shrewsbury.
