Defending a total of 165, they dismissed their opponents for 104 in 16.2 overs, although Essex at least had the consolation of joining their victors in the last eight by being one of the best two third-placed sides.
Surrey's triumph was built upon a fine innings from opener Steve Davies. After watching Jason Roy and Vikram Solanki depart in Graham Napier's first over with only 12 on the board, Davies struck a punishing 54 from only 27 balls.
His knock included six fours and three sixes, and once he was caught in the deep attacking David Masters, Zander de Bruyn (39) and Gary Wilson (43) ensured a challenging target.
Both were removed by paceman Reece Topley, who finished with three for 40 to take his number of scalps in this season's competition to 19, the highest in the country. But it was his pace colleague Graham Napier who emerged as the most successful bowler as he returned to polish off the innings and finish with four for 18 from four overs.
Essex slumped to 52 for seven in reply, and despite a brave and belligerent innings of 60 from just 39 balls from Ryan ten Doeschate that spared his side utter humiliation, the home side's response came to an end with 22 balls remaining.
Sean Ervine's first half-century of this season's competition enabled holders Hampshire to overcome Middlesex's plucky challenge at the Ageas Bowl by eight runs and set up a home quarter-final against Lancashire next week.
Ervine hit an unbeaten 60 and shared in a stand of 101 in 9.5 overs for the fourth wicket with consistent veteran Neil McKenzie who made 47 not out as Hampshire accelerated over the second half of their innings to reach a formidable 190 for three.
But Middlesex, who needed to win to stand any chance of qualifying for the latter stages, were undaunted and came desperately close to causing an upset by finishing with 182 for seven thanks to Joe Denly's belligerent 67 and a rapid 29 from Eoin Morgan.
Sussex Sharks' dismal T20 campaign ended on a suitably downbeat note as Kent Spitfires condemned them to a ninth defeat in this season's competition.
The hosts were bowled out for 113 off the final ball of their innings and Kent eased to an eight-wicket victory with 41 balls to spare to ensure Sussex finished bottom of the South Group.
Quarter-finalists for the last four years and one of the pre-tournament favourites, Sussex's campaign never got any momentum and a woeful batting performance was typical of their efforts in this season's tournament.
Mitch Claydon took three for 22 for the visitors, who made light work of chasing their target as Matt Coles top scored with 40 from just 23 balls.