The Town defender turned in 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.
Shrewsbury boss Micky Mellon brought in 17 players in the summer, after only arriving in May himself, with the side made up of homegrown players, free transfers and two loanees.
Only striker James Collins cost a nominal fee from Hibernian.
And front of a record crowd at Greenhous Meadow - 10,210 - the Sky Bet League Two side rattled a Chelsea team containing four Champions League winners and a World Cup champion.
Just Drogba, Gary Cahill, Filipe Luis and Oscar survived from their 1-1 draw at Manchester United while defender Andreas Christensen was given his Blues debut.
James Wesolowski, who had been nursing a groin injury, was replaced at the last minute by Liam Lawrence despite being named on the Shrewsbury team sheet.
It was their only change from a 2-1 win over Portsmouth on Saturday which took Town to fourth in League Two.
It was their fourth straight win and 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 initiative, ingenuity and enthusiasm worried Chelsea.
In the middle Ryan Woods dictated from deep while skipper Connor Goldson won his first-half battle with Drogba.
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 Mohamed 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.
It fell to the massed ranks of, grateful, Shrewsbury defenders but it was a warning.
Salah's wild strike then flew out for a throw to underline Chelsea's frustration as they struggled to breach the hosts' organised backline.
When they did, three minutes before the break, Drogba was offside after steering the ball past Leutwiler following Oscar's mis-hit.
There had been little to concern Shrewsbury in the first half but within three minutes of the re-start they were behind.
Schurrle and Salah combined well to tee up Drogba who clinically steered past Leutwiler from 12 yards.
It was the first goal Shrewsbury had conceded in the competition but they almost levelled eight minutes later.
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 with Chelsea content.
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 to end home hopes.
Source : PA
Source: PA