The 18th-ranked Thais needed to win against the 51st-ranked Solomons to guarantee their berth in the knockout stage at Žalgiris Arena in Kaunas, Lithuania.
Suphawut Thueanklang helped Thailand on their way by scoring a hat-trick against the Pacific islanders.
Meanwhile, Portugal and Morocco drew 3-3 in the other group C match. Thailand qualified by grabbing third place in the group with 4 points.
The Thais face Kazakhstan in the round of 16. The match will kick off on Thursday at 9.30pm, Thai time.
Related News
Jirawat timely strike helps Thailand force a draw in futsal World Cup
Thailand beaten by Portugal in futsal World Cup
Major international tournaments get CCSA green light
Kazakhstan are currently ranked seventh in the world.