Essex went into the game against Surrey having lost their previous two, but Scrivens and Winfield-Hill gave home followers cause for optimism with 13 boundaries between them before the former was caught at cover off Dani Gregory.
Winfield-Hill - who was dropped on seven - followed in the next over when she tried to sweep Harris and top edged to fine leg, but it was a spell by Farrant which sent the innings into decline.
She bowled Lissy MacLeod behind her legs with a looping yorker and had Cordelia Griffith caught at deep mid-wicket next ball.
Farrant thought she had a hat-trick as she appealed for leg before against Jo Gardner, but the umpire had spotted a thin edge - but the left-armer (3-20) had Maddie Penna caught in the deep in her next over.
Harris rounded off the innings by taking return catches offered by Gardner and Eve Gray - and there were two in the same over by Esmae McGregor as Bryony Smith and Alice Capsey fell to successive balls to leave them 31-2 in their chase.
There was further encouragement for Essex when Danni Wyatt-Hodge (21) hit Aftaba Maqsood to mid-off, but Chathli and Harris (31) added 40 in three overs and even though both departed as McGregor returned 3-33, Davidson-Richards and Phoebe Franklin finished the job.
"We weren't at our best on Wednesday (against the Blaze) but these games come thick and fast. It's important to get back to winning ways as quickly as possible," Farrant said afterwards.