The first half was devoid of too many clear-cut chances, although both sides could have been in front at the break.
Lee Holmes curled an effort narrowly wide for Exeter, while James Hamon made a terrific save to keep out an effort by Dagenham’s Matt Partridge.
Clinton Morrison was off target with a volley for the hosts before Ashley Chambers saw a spectacular curling effort ruled out for offside.
Eventually, the deadlock was broken after 61 minutes when substitute Jimmy Keohane found a yard of space and curled a delightful effort into the top corner of the net with his left foot from 25 yards.
Top scorer Tom Nichols then notched his 15th goal of the season for Exeter after 70 minutes when he seized on a shocking pass by Ian Gayle for a simple tap-in.
Morrison almost added a third for the Grecians but former Exeter striker Jamie Cureton turned in Ashley Chambers’ cross for his 20th goal of the campaign in stoppage time for a consolation for the Daggers.