Essex made light work of the Unicorns to maintain their unbeaten start to life in Group C of the Clydesdale Bank 40.
After wins over Nottinghamshire and Lancashire and a washout at Glamorgan, the Eagles surged to an eight-wicket win against their semi-professional opponents at Bury St Edmunds.
The Unicorns, by comparison, have now lost four consecutive matches in the competition and remain rooted to the foot of the table.
Their batting let them down once again on Sunday afternoon, Chris Benham's 58 was the only bright spot as the Unicorns were dismissed for only 137 inside 38 overs.
Slow left-armer Tim Phillips recorded competition-best figures of 5-28 for Essex, who had little trouble knocking off the runs.
Newly-appointed England one-day captain Alastair Cook and Mark Pettini put on 53 for the first wicket before Neil Saker removed the former for 38.
Graham Napier (11) also departed, however Pettini (48 not out) and Ravi Bopara (29no) safely guided Essex home with eight wickets and 35 deliveries remaining.