Thunders, chasing Sixers’ 150-run target, required 15 off the last over and Arjun Nair hit two back to back fours off Sean Abbot’s first two balls.
The match went down to the last ball with Thunders requiring one run off the final ball.
Nair scored the winning runs as he swatted Abbot to cover for a single.
The chase, however, was made possible by a 46-ball 77 by veteran batsman Shane Watson.
Watson walked to the crease earlier in the piece as Jos Buttler was caught and bowled by Daniel Sams on the last ball of Thunders’ 150-run chase. He struck 12 boundaries – six 4s and six 6s.
Earlier, Sydney Sixers scored 149/9 with Nic Maddison and Sam Billings starring with 31 and 32.
Brisbane Heat will host Melbourne Stars in the second game of the season on Tuesday.