The League Two outfit enjoyed the better of the game in the first half, but Chelsea responded after the restart as Didier Drogba converted from 12 yards.
A minute after being introduced as a substitute, Andy Mangan equalised for Shrewsbury to give his team hope before Grandison turned in Willian's cross to ensure that Jose Mourinho's side avoided an upset against a club who sit 72 places below them on the league ladder.
Read below to see how the action unfolded on Tuesday night.
7.16pmHello, and welcome to Sports Mole's live coverage of the match between Shrewsbury Town and Chelsea in the fourth round of the League Cup.
7.18pmAt the start of the competition back in August, Shrewsbury Town would have probably been happy with an appearance against a Premier League side in the second round before focusing on league matters. However, after defeating Leicester City and Norwich City, the Shropshire-based club are just over 25 minutes away from going toe-to-toe with the Premier Leaguer leaders at the Greenhous Meadow!
7.21pmIt's a fixture that has really captured the imagination in Shrewsbury. Tickets went almost instantly, with a member of the boardroom revealing that they could have sold out of tickets five times over, and the demand from the locals has seen the League Two team install a temporary stand to enhance their capacity. Chelsea are the overwhelming favourites but after their previous victories and current form in the league, Micky Mellon's players will fancy this tonight.
7.22pmAfter playing Manchester United at Old Trafford just over 48 hours ago, all eyes would have been on Jose Mourinho's team sheet when it was revealed half an hour ago. There are seven changes to his starting lineup, but it's a lot stronger than you might have imagined...
7.24pmCHELSEA SUBSTITUTES: Schwarzer, Terry, Matic, Baker, Willian, Hazard, Brown
7.27pmThe likes of Thibaut Courtois, Cesc Fabregas and Diego Costa are all absent for the Blues, but that's a pretty formidable lineup, and an experienced one at that. As for the youngsters, Kurt Zouma gets another chance to impress, Nathan Ake will be keen to make an impact in a rare start while Andreas Christensen, who impressed for Chelsea during their Under-21 Premier League success last season, makes his first start with the senior team.
7.29pmSHREWSBURY TOWN SUBSTITUTES: Burton, Ellis, Vernon, Lawrence, Griffith, Mangan, Clark
7.32pmYou are all likely to be pretty familiar with Chelsea's league form, but what about Shrewsbury? They are currently sitting in fourth place in League Two having registered 27 points from 15 games, 12 of which have come in their last four outings. They are also yet to lose at the Greenhous Meadow, with seven of the eight contests ending in a home win. Maybe Chelsea won't have it all of their own way this evening?
7.35pmPREDICTION! In front of what is a record attendance, the Shrewsbury players are going to want to start at a high pace to ruffle a few feathers within the Chelsea ranks. However, once the action slows down, the quality of Mourinho's men should shine through and it would come as a major surprise if they don't prevail by least a couple of goals. 4-1 to Chelsea.
7.38pmAs ever, we are all over tonight's action up and down the country. If you want to take a look at our selection of live text commentaries, click here.
7.42pmThe two teams are about to make their way out onto the pitch in front of a crowd of nearly 10,500. Shrewsbury could need each of them to help them have a chance of pulling off one of the greatest shocks in the history of this competition.
7.45pmWe have a late change in the Shrewsbury lineup. The experienced Liam Lawrence has come in for James Wesolowski, who was a fitness doubt before the game.
1 minShrewsbury get this League Cup fourth round fixture underway.
3 minChelsea spend the opening moments spraying the ball around with ease as Shrewsbury remain content with sitting back in their own half. On Chelsea's first attack, Filipe Luis whipped a teasing cross into the middle for Didier Drogba, but the ball is well deflected out for a corner.
5 minCHANCE! Straight from the corner, Shrewsbury break with pace and James Collins manages to earn a welcome corner for his side. It's a terrific ball into the area from Liam Lawrence which finds Nathaniel Knight-Percival, who sees his eight-yard header well tipped away by Petr Cech.
7 minUnderstandably, Shrewsbury are well up for this. A long ball down the right flank sees Jean-Louis Akpa Akpro beat Gary Cahill to the ball but his pullback into the six-yard box is claimed by Cech.
10 minChelsea take their chance to slow things down a notch to spend a bit more time in possession. Andre Schurrle has had a weak shot on goal deflected straight into the hands of Jayson Leutwiler, but that's about it for the top-flight leaders during the first 10 minutes.
13 minSHOT! Shrewsbury regain the ball and immediately set about advancing forward. The ball is played into Bobby Grant around 30 yards from goal, but the on-loan Blackpool attackers' strike is always rising and it clears Petr Cech's crossbar by several yards.
16 minThe likes of Oscar and Didier Drogba have barely have a kick. Oscar is struggling to get a foot on the ball while Drogba is being muscled out of it - yes, you read correctly - muscled out of it by Jermaine Grandison.
17 minSHOT! Mohamed Salah has been equally as quiet but he cuts inside onto his left foot to get a shot away from 25 yards. Unfortunately for Chelsea, it's a dismal attempt, with the ball curling a number of yards past the top corner.
21 minBOOKING! The first man into the referee's notebook is Nathan Ake and deservingly so. The youngster has lost the ball on a few occasions and he takes his frustration out on Bobby Grant by sliding in late on the Shrewsbury man.
24 minI'm sure that Jose Mourinho only intends on using the likes of Eden Hazard and Willian in the event of an emergency but they could very well be needed if we continue like this. Chelsea are offering nothing in the final third, and for a team of such quality, that is going to annoy the Portuguese coach.
26 minThat said, a lot of the credit for Chelsea' lack of success should go to Jermaine Grandison, who is bossing Didier Drogba and co at the moment.
30 minWe have reached the half-hour mark at Greenhouse Meadow and we remain goalless. There has been a lack of goalmouth action but the contest have been intriguing nonetheless. Shrewsbury aren't overawed by the occasion and have been the better team by far.
32 minChelsea finally have some joy in the final third. Mohamed Salah accelerates clear of the Shrewsbury defence before crossing to the back post for Andre Schurrle. However, for reasons only known to the German, he attempts to head the ball back across goal rather than on target and the chance disappears.
36 minThe last few minutes have seen Chelsea start to find a bit more rhythm which is keeping Shrewsbury penned in their own half. Mohamed Salah is also seeing more of the ball but apart from the cross to Salah, his distribution has been poor.
39 minWe have almost reached half time and we are yet to see a goal in any of the five League Cup fixtures. Fingers crossed for the second half...
42 minMohamed Salah, please, just give up. For the third time tonight, he cuts inside onto his left foot to get a shot away and this attempt is the worst of the lot, and that's saying something. His efforts goes out for a throw in, much to the delight of the home support.
43 minChelsea have the ball in the net, but Didier Drogba is rightly adjudged to have been offside. Still, it's progress for the Londoners.
45 minAndre Schurrle wins a corner for his side, and his set piece finds the head of Gary Cahill, but the centre-back's attempt is blocked by a defender. There shouldn't be too much added-on time at the end of the half.
8.33pmThe half-time whistle goes at Greenhous Meadow and Shrewsbury Town have easily held Chelsea during a superb first-half performance. Jayson Leutwiler hasn't been tested in the Shrews' goal, and that something that Jose Mourinho will be keen to change after a stern telling off at the break.
8.37pmChelsea have had 63% of possession and eight shots to Shrewsbury's four, but this is a perfect example of not always believing statistics. The League Two side have done more with the ball, with Jean-Louis Akpa Akpro posing problems for Gary Cahill and Kurt Zouma. There was also the header from Nathaniel Knight-Percival that tested Petr Cech, so they can perhaps count themselves unlucky not to be leading a team 72 places above them in the league pyramid.
8.41pmIt wouldn't come as a surprise if Mourinho made an alteration at the break. Chelsea need someone to stamp their authority on the game. Nemanja Matic or Eden Hazard could be the ideal choices to replace Nathan Ake or Mohamed Salah.
8.45pmMourinho has chosen against moving early in terms of any changes. I'm sure it won't take him long to tinker with his team if things don't improve though.
46 minChelsea have got us back underway in the second half.
47 minShrewsbury want a foul after a 50-50 challenge, but nothing is given and Oscar sends a deflected strike wide of the post. The Blues look sharper here...
48 minI get the impression that Chelsea have been given a ticking off from their manager. The Premier League leaders take the lead through Didier Drogba, who meets Mohamed Salah's knockdown to send a half-volley into the back of the net from 12 yards. Will that goal open the floodgates...
51 minSHOT! Andre Schurrle has remained on the periphery of the game but he unleashes a venomous 30-yard strike that forces Jayson Leutwiler into a excellent finger-tip save to send the ball over the crossbar.
54 minShrewsbury are attempting to meet Chelsea's rapid start with one of their own, but it's a dangerous game to trade with the Stamford Bridge outfit. Space is beginning to open up for Mohamed Salah and Oscar, and that could spell trouble for Micky Mellon's men.
55 minCHANCE! So, so close for Shrewsbury! The ball rebounds favourably for Jean-Louis Akpa Akpro who sends a volley towards goal, but his effort is deflected inches wide by James Collins. Petr Cech would have been able to do nothing about that if it was on target.
59 minSAVE! Jayson Leutwiler was barely needed during the first half, but he keeps Shrewsbury in the game with by punching Didier Drogba's stinging strike wide for a corner. It's been a very lively start to the second period.
62 minWe are two thirds through this League Cup contest and in the space of 15 minutes, it's Shrewsbury boss Micky Mellon who is probably considering an alteration. A record attendance of 10.210 for the Greenhous Meadow has just been announced.
65 minJack Grimmer is lucky to avoid a booking after a studs-up challenge on John Obi Mikel, but the referee plays the advantage for Chelsea to win a corner after a Filipe Luis cross is sent behind. However, nothing comes from the set piece as Shrewsbury clear.
67 minSUBSTITUTION! The first change of the night comes from Shrewsbury, who introduce Jordan Clark for Bobby Grant. Still no move for Mourinho.
70 minShrewsbury haven't had any play in the final third for the last 10 minutes. They could be paying the price for such a high-tempo pace that they have played at during the opening three quarters of this encounter.
73 minThe same could be said of Chelsea. They are still passing the ball about with ease in all areas of the pitch, but shots have been few and far between since the hour mark.
75 minSUBSTITUTION! Micky Mellon makes his change of the night, bringing on Andrew Mangan for James Collins. Can he have an impact during the final 15 minutes?
77 minThe answer to that question is yes! Unbelievable scenes at Greenhous Meadow. A corner from the left was headed towards goal by Jermaine Grandison, and after that was blocked by John Obi Mikel, the ball rebounded to Mangan who lashed the ball home from close range.
79 minSUBSTITUTIONS! Jose Mourinho's reaction? He throws on Willian and Nemanja Matic for Mohamed Salah and John Obi Mikel.
81 minGOAL! Shrewsbury Town 1-2 Chelsea (Grandison own goal)
81 minFor the second time in the space of a few minutes, a substitution makes an immediate impact. An inswinging cross from Willian was about to find Didier Drogba, but Jermaine Grandison stuck out his leg to divert the ball in off the far post. To be fair to the 23-year-old, he had little choice but to try to intervene, but it's put his team behind for the second time in the match.
84 minThis match is far from over, but it's going to take some effort from Shrewsbury to respond again. Chelsea are asserting themselves on this match now.
87 minMore keep ball from Chelsea has Shrewsbury chasing shadows trying to regain the ball and in turn, wasting more of the energy that is left in the tank. It's not pretty, but it's effective.
88 minCHANCE! The League Two side do get the ball back and quickly engineer an opening. Ryan Woods sends the ball into the box for Jean-Louis Akpa Akpro, but his header goes wide of the far post.
90 minJermaine Grandison has been sent up front in an attempt to cause some aerial problems for Kurt Zouma and Gary Cahill, and he has some success by nodding on a high ball, but Petr Cech comes out to claim. There will be three minutes of added-on time.
90+2 minAndre Schurrle breaks clear on the left flank, but inside of using Oscar, he opts to go the direct route before blazing over from 12 yards.
9.38pmThe final whistle goes at Greenhous Meadow and Chelsea have fought their way past Shrewsbury Town to advance through to the quarter-finals of the League Cup. They didn't have it all of their own way against the League Two outfit, but an improved second-half performance got the job done in the end.
9.40pmThis match might be over but we hope that you head on over to the game between Liverpool and Swansea City at Anfield. Swansea are currently leading thanks to a goal from Marvin Emnes!
9.42pmThat will be all from Sports Mole for this fixture. Thank you for joining us this evening, and we hope to see you again tomorrow night where the game between Manchester City and Newcastle United headlines the remaining ties in the League Cup. Goodbye for now.