The victory was Thunder’s first of the season as Max Richardson sank 13 points and captain Bud Johnson and Jack Sunderland scored ten each.
Worthing coach Daniel Hildreth said: “It’s important for the team and the confidence and the morale to get our first win.
“We didn’t play to the potential that we would have liked but we got the job done and that’s the most important thing.”
Thunder travel to Plymouth Marjon Cannons in the next round on Sunday.
To watch highlights of the win against Team Solent, click on the video above.