Dagenham looked set to avoid defeat on their third visit to the Prostar Stadium - but right at the death of this often untidy encounter, Holt notched his 17th goal of the campaign to keep Shrewsbury right among the League Two pacesetters.
After a 4-0 defeat at the same ground last season and a 5-0 reversal on November 4, Dagenham were only seconds away from ensuring a point after a 78th-minute leveller by Sam Saunders had cancelled out a 50th-minute goal from Jamie Blake.
But John Still's men, keen to build on their 6-1 demolition of Notts County at the weekend, were denied a share of the spoils by Holt's late, late winner.
Despite dominating long periods of the first half, high-flying Shrewsbury, unbeaten in their last five league games, were unable to create any clear-cut openings and the visitors made it through to half-time without any undue alarms.
But that all changed five minutes after the break when a smart move involving midfielder Paul Murray and Holt created the opening for young striker Blake - who joined Shrewsbury on-loan from Southampton last week - and he scored with a fine low drive from the edge of the box.
But 12 minutes from time Saunders equalised in impressive fashion, curling home a free-kick from 20 yards and Dagenham, despite a couple of late scares looked set to leave with an unlikely point.
However, with only seconds remaining Shrewsbury substitute Dave Hibbert was sent crashing in the box following a challenge by Dagenham's Ben Strevens - and up stepped Holt to convert the ensuing the penalty to give Shrewsbury victory.