Compton was next to be dismissed with the total on 247 after scoring his 55 off 64 balls but Buttler and Suppiah added some late fireworks to send Somerset out of sight.
Flower clipped the ball off his legs to deep square leg and attempted a second run, only to find himself short of his ground when Buttler fired the ball in for wicketkeeper Kieswetter to remove the bails.
But, in the same over, he went for another big drive and was caught inside the long on boundary by Buttler for 58 off 38 balls - and that prompted a collapse of five wickets for just nine runs as the Essex chase ended abruptly.