After a narrow win over Lancashire on Monday, Holland picked up their fourth victory of the fledgling 40-over tournament as rain delays reduced play to 36 overs a side.
Timm van der Gugten set the tone for the hosts by dismissing Mark Pettini and Owais Shah in the opening three balls of the day.
Alviro Petersen followed shortly afterwards as Van der Gugten claimed a third victim.
Tom Westley (32) and Graham Napier (27) were the only Essex batsmen to record decent scores before Ahsan Malik removed both.
The wickets of Tim Phillips and Charl Willoughby sandwiched Napier's as the visitors were bowled out for 112 in the 34th over.
Michael Swart followed up his 41 runs against Lancashire on Monday with a match-winning 40 before finally being bowled by Phillips.
Tom Cooper (22) also fell to Phillips after opener Stephan Myburgh had been caught off the bowling of Napier in the second over.
Mudassar Bukhari could not find the winning runs as he was dismissed with the scores level.
The victory was soon confirmed as Napier delivered a wide with the second ball of the 23rd over to gift Holland victory with 83 balls remaining, to leave Essex still searching for a win in Group A.