Glamorgan lost 10 of them as they were dismissed for 231, Stewart Walters (67) and Jim Allenby (77) making the majority of those runs.
David Masters was Essex's main threat and ended with five for 44, before Michael Hogan hit back twice for the hosts to leave the away team 10 for two.
Leicestershire managed four wickets despite only 34 overs being possible on a rain-affected day against Northamptonshire.
The home side made 91 for four in the time available, with Ollie Freckingham taking two wickets.
Rob Newton, on 22no, is already the top scorer of an innings that has thus far failed to get going.