Essex 325 for 6 (Browne 99, Bopara 59, Ryder 50) beat Glamorgan 324 for 8 (Ingram 107, Lloyd 62) by four wickets
Nick Browne posted his highest List A score to keep Essex top of the Royal London Cup South Group table, but the opener might have been celebrating a first 50-over hundred if he had not been run out on 99.
Browne slipped as he turned for a second run and failed to beat home Andrew Salter's throw from deep mid-on. He had faced 104 balls, and in partnerships of 82 with Jesse Ryder and 85 with Ravi Bopara laid the foundations for Essex to chase down 325 with five balls to spare.
The left-hander's previous best had been the 69 he recorded against Hampshire at Southampton last year. Coincidentally, Browne's previous highest score in this season's competition was 49 before he was stumped in the win against Kent.
Ryder and Bopara both contributed half-centuries and Ryan ten Doeschate and James Foster thrashed 36 off 20 ball to finish the chase as Essex claimed their fourth win in six games after their 66-run defeat by Surrey on Sunday.
That Essex faced such a big target was down to a 66-ball hundred by Colin Ingram, containing six sixes. The South African needed just 73 balls to reach 107 - which also included seven fours - and dominated stands of 83 and 87 with Will Bragg and Graham Wagg for the third and sixth wickets.
Ingram took 41 balls to reach his half-century, and then accelerated to the extent that his next fifty took just a further 25 deliveries. But the biggest partnership of Glamorgan's innings went to openers David Lloyd and Jacques Rudolph, their 105 partnership spanning 23 overs.
Four of Essex's seven bowlers went for more than seven an over, and only the steady David Masters kept Glamorgan under control with two for 44 from his 10 overs. Graham Napier finished with three wickets, but at a personal cost of 73. In the end it mattered not.