Wells caption Chris Williams won the toss and chose to bat, and he soon showed his handsome form, racing to 48 from 38 balls with nine fours.
But when Andrew Faulkner (3 for 16) castled him, the innings capitulated with Nick Wheddon (3 for 34) grabbed three wickets in four balls.
The visitors collapsed from 64 for 1 to 80 for 7 until Christian Davis, with a watchful 41 from 77 balls, finally found a partner in veteran wicket-keeper Simon Routh in an eighth-wicket stand.
But the damage had been done, and Wells were all out for 115 with more than 10 overs unused.
They fought like tigers, and managed to make the home batsmen work hard as they crept past the required total.
Paceman Ari Karvelas (2 for 28) and spinner Marcus O’Riordan (2 for 24) caused a wobble.
But there were just too few runs to play with and HSBC reached 117 for 7 after 32.1 overs.
Wells now face Bickley Park at home on Saturday (June 29).
Linden Park win T20 local derby
Tunbridge Wells had already been left licking their wounds following a surprise exit from the Kent Twenty20 Cup to neighbours Linden Park on the Upper Common.
The latter won the toss and batted first, raising 142 for 5 thanks to Freddie Hulbert’s unbeaten 62 and Tom Corner (43).
Ian Mclean was the pick of the bowlers, returning 3 for 30 in his four overs.
Wells’ run-chase fell short on 131 for 7 despite the efforts of Sam Watts, who remained undefeated on 26 at No 8, and Jorge Ehren (13 not out) at No 9.
Carlin Tapp caused the principle damage with 3 for 13 while Oliver Bone picked up 2 for 25.