Thunder were up by 10 points in the third quarter but Westminster fought back and drew level at 83-83 with 22 seconds to play.
Courtney Small then held the ball to run down the clock and drove to the hoop to score with 0.6 seconds left on the clock.
Westminster then called a double timeout, one straight after the other. Warriors passed the ball to Edmir Lucas, who thought he was fouled as Small went to block his shot attempt. Had the foul been given, Warriors would have had three free throws but the referees called a halt to the game which meant Thunder were victorious.
Thunder captain James Brame said: “It looked like the referee had called a foul but he in fact had called time.
“If they’d been given a foul, I guarantee that Lucas would have made all three free throws as he was hot all game.
“It was a tough game in a hostile environment at one of the older venues that we play at and we’ve had two tough games there now.
“They play hard and had Marvin Addy and Damian Harris, who used to play for us, which maybe meant they played that bit harder, but we put in a good team performance in a tough environment.
“There’s no easy games in this league and, coming down from the BBL, we’ve got that target on our back so everyone wants to beat us.
“We are still a work in progress, although we’ll keep building and will be a hard team to beat as the season goes on.”
Marcus Tullis added: “Any time you get a win, you have to be happy with it, but it was an ugly game on our end.
“I think the overall defence was a bit lacklustre and as a team we all have to step it up.”
Thunder led 26-21 at the end of the first quarter and were 47-39 up at half-time.
Westminster fought back to trail 62-59 at the end of the third stanza, before Thunder held on to win.
Liam Mitchell led Thunder’s scoring with 18 points, supported by Vinnie Darpino, who hit 17, and Tullis, who scored 16. Small and Hank Rivers both added 13 points but Westminster’s Lucas led all scorers with 40 points.
Brame added: “Liam was aggressive offensively and it was good to see. Jack Sunderland also came on and did well defensively against Lucas.
“That’s what I like to see – local guys being given a chance.
“They’re proving that they should be out there and it bodes well for the future.”
Thunder host Tees Valley Mohawks on Saturday at Worthing Leisure Centre (7.30pm) and then travel to Medway Park Crusaders on Sunday (3pm).