The England captain has apparently shaken off the frustrations of the winter with some fine early-season scoring, and proved his touch against the tourists by blazing 71 in 49 balls.
That led Essex to 161 for five, after the match had been reduced to 21 overs a side by rain, before a near full-strength Sri Lanka side came up short.
On-loan seamer Oliver Newby claimed 3-36 after taking the new ball, including the key wicket of veteran Mahela Jayawardene.
Sri Lanka were fresh from their 1-0 ODI series win over Ireland in Dublin and, while they were denied a full 50-over contest, the weather did at least allow them preparation for next week’s NatWest International T20 against England at the Kia Oval.
Cook will not play a role in that game, but the left-hander proved he is hitting the ball as well as anyone at the moment.
The 29-year-old struck four fours and cleared the ropes twice to kick-start Essex.
Cook had been less fluent when making 44 in the 39-run Duckworth/Lewis method win over Scotland in last Friday’s Royal London one-day international at Aberdeen, but with Ben Foakes also in full stride he found his range.
Foakes blasted 51 from 31 balls in an 82-run stand with Cook, which proved critical as Sri Lanka struggled in pursuit.
Newby did the early damage as he trapped the dangerous Kusal Perera in front from the fourth ball of the innings, before Foakes held on to see off Jayawardene.
Dinesh Chandimal top-scored for the tourists with 31, but he too fell victim to Newby as Sri Lanka finished their 21 overs on 146 for nine.