Poland's Chwalinska was handed a wild card for Wimbledon after her stellar Roland Garros run, which also ensured that the 24-year-old was seeded 20th at the All England Club.
She looked to be cruising after winning the first set and was a point away from a routine win while ahead 5-2 and 40-30 in the second set when she slipped and fell awkwardly near the baseline to injure her right ankle.
Chwalinska fought on in the second set but struggled to move freely and allowed Sawangkaew to draw level at one set apiece, before her challenge faded again after she squandered a 2-0 lead in the decider.
World number 164 Sawangkaew held her nerve in the face of a valiant fight and sealed the win for her first Grand Slam main draw victory.