As penalty runs prove crucial as narrow victory in the last over
to stem the flow of runs, a ploy which accounted for Bracey and the dangerous Ryan Higgins and caused Gloucestershire to lose crucial momentum during the middle overs.
Heavily dependent upon Cockbain, Gloucestershire were indebted to the Liverpudlian, who punished anything short of a length in raising 50 from 41 balls to keep his side in the game.
When big-hitting Jack Taylor missed a straight delivery and was pinned lbw by Jordan in the 16th over, it was left to Howell to provide late acceleration, the veteran all-rounder scoring at two runs a ball in a valuable sixth-wicket stand before holing out to long-on off Robinson in the final over.
Cockbain finished unbeaten on 61 from 49 balls but not even his innings could dispel the feeling that Gloucestershire had fallen short.
But Sussex found the going equally difficult on a two-paced pitch, Philip Salt and Laurie Evans succumbing to David Payne and Andrew Tye respectively as Gloucestershire made good use of the new ball.
Sussex remained favourites until skipper Luke Wright, having compiled a painstaking 24, lost patience and holed out to long-on off the bowling of Tom Smith.
The visitors were 87 for four in the 13th over when Australian international Alex Carey played across the line and lost his off-stump to Chris Liddle.
Dropped by Cockbain at backward point on 11, David Wiese threatened to dig the visitors out of a hole until falling lbw to Payne for 37 with the score on 126 in the 17th over.
Tye then returned to dismiss Rashid, while Jordan holed out to long-on in the penultimate over as Payne finished with three for 35.
But the six-run penalty ensured Sussex were favourites going into the final over and Rawlins needed no second invitation.