Two goals in the space of nine first-half minutes from Napat Tamrongsupagorn and Dragan Boskovic gave the visitors a comfortable lead.
TOT were unable to respond and remain just three points clear of the drop zone, having played a game more than their rivals near the foot of the table.
Suphanburi stay fourth but are now four points ahead of Bangkok Glass.
Tamrongsupagorn opened the scoring in the 18th minute, with Boskovic doubling Suphanburi's advantage soon after.
Goals have been a problem for TOT all season, with only Samut Songkhram scoring fewer in the top flight, and there was to be no riposte from a team who have now lost five of their last seven.
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