Paiboon Lertwimolrat's men only had five points heading into Saturday's encounter at the TOT Stadium Chiang Wattana, but the visitors ended a five-match losing league streak.
Sarif Sainui opened the scoring in the 37th minute and Songkhram held onto their advantage until the break.
Both sides were reduced to 10 men just after the hour when Lee Jun-Ki was dismissed for the hosts, while Adison Daeng-rueng saw red for the away team.
Sainui then doubled the lead with his second to calm Songkhram's nerves and, though Mohamed Kone reduced the arrears in the 76th minute, the visitors hung on for victory.
At the other end of the table, league leaders Muang Thong United were held 0-0 at home by AFC Champions League hopefuls Army United.
Suphanburi moved up to third ahead of Army United, Alexandre Polking's men triumphing 2-0 at home over Chainat, Napat Thamrongsupakorn scoring in each half.
Also on Saturday, reigning champions Buriram United were comfortable 3-0 victors over strugglers Bangkok United, while Air Force United defeated 10-man Sisaket 2-0.
On Sunday, BEC Tero Sasana moved level with Muang Thong at the top of the table thanks to a comfortable 3-1 home win over Singhtarua.
Honduran striker Georgie Welcome and Narubodin Weerawatnodom handed the hosts a two-goal cushion by half-time, while Rangsan Viwatchaichok made the game comfortable in the 66th minute.
Kim Geun-Chul grabbed a 77th-minute consolation, but it mattered little as BEC remained unbeaten in the league this term.
In a battle between two strugglers, PTT Rayong routed Songkhla United 4-0 in what was just their second win of the season.
Amadou Ouattara was the standout performer with in hat-trick as all four goals came in the second half.
Chonburi and Chiangrai boosted their hopes of qualifying for continental competition, the former defeating Osotspa 2-1, while the latter overcame Police United 2-0.
Rounding off the action, Heberty took home the match ball as his hat-trick helped Ratchaburi to a 4-2 success at Bangkok Glass.
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