Sussex made the most of bowling first on a used pitch as they skittled a Glamorgan for 101 in a 14-overs game.
The home side had reached 30-1 when the rain arrived after one ball of the fifth over - five deliveries before a result could have been calculated.
No more play was possible and the match was abandoned.
Winning the toss was crucial for home captain Luke Wright and after an eccentric first 10-ball over from Mills, Glamorgan turned in a woeful batting performance with 26 extras the main contributor.
Garton, who had not previously taken a T20 wicket, made the most of difficult conditions, claiming four wickets, while Matt Machan took five catches including a superb boundary effort to dismiss Aneurin Donald.
Last pair Michael Hogan and Shaun Tait scrambled the total into three figures before Chris Jordan finished the innings off.
The weather closed in after four overs of the Sussex reply, and although the umpires managed to get the players out for one further ball, a heavier downpour brought an end to the game, to Sussex's frustration.
Glamorgan claimed a home tie in the quarter-finals of the T20 Blast in bizarre circumstances as rain saved them from defeat against Sussex.