Essex 213 for 1 (Cook 92*, Westley 87*) beat Middlesex 212 (Davies 70, Snater 3-45) by nine wickets
England legend Cook clocked his 48th List A fifty to end 92 not out while Eagles captain Westley returned an unbeaten 87, the pair putting on 159 together.
Essex were only chasing 212 after Shane Snater's 3 for 45 and two-fors for Simon Harmer and Ryan ten Doeschate, and completed a comprehensive victory with 11 overs to spare to maintain their 100 per cent record in the competition.
Westley won the toss and restricted Middlesex to a below-par 212, with runs not flowing particularly freely on a green-tinged wicket under thick grey clouds.
Sam Robson was the exception to the rule has he stroked 18 in nine balls before he was strangled down the leg-side by Snater. Joe Cracknell was leg-before to Snater and Australian Peter Handscomb was excellently snaffled at first slip by Cook as the visitors slumped to 31 for 3.
Middlesex then produced their two, much needed, partnerships of note as Max Holden and Robbie White added 49 before Holden top-edged a sweep to the short boundary and was replaced by Jack Davies, who put on 67 with White.
Neither White nor Davies scored at any great speed but ticked along, the former falling for 47 lbw to Paul Walter, while List A debutant Davies reached his half-century in 67 balls.
Middlesex lost their last five wickets for 39 runs as Luke Hollman was lbw to Westley, James Harris chipped straight back to Harmer, Thilan Walallawita edged ten Doeschate behind and then the Dutchman produced cat-like reactions to pouch a return from Davies. Snater ended up at the top of the wicket pile, returning 3 for 45, as Ethan Bamber pulled into the leg side to end the innings.
Essex's chase looked in little doubt from the moment Will Buttleman cut Walallawita to the boundary with the fourth ball. Cook looked in sumptuous form with pure timing trumping outright power. An on-drive through midwicket, a straight drive and a push through the off side typified his style and got him motoring.
Buttleman flicked straight to Robson at short midwicket, having put on 54, with Cook in a rare batting misjudgement from the hosts. Cook reached his 20th format fifty for Essex in 60 balls with a flick off his legs, with Westley unfurling some glorious stroke play as the duo reached a century partnership in 118 deliveries.
Westley moved to his half-century in 59 balls before threatening to overtake his experienced partner, and eventually preventing him from reaching three figures.