Wikipedia has your answer:
It seems paradoxical to treat an extreme diuresis with a diuretic, but the thiazide diuretics will decrease distal convoluted tubule reabsorption of sodium and water, thereby causing diuresis. This decreases plasma volume, thus lowering GFR [glomerular filtration rate] and enhancing the absorption of sodium and water in the proximal nephron. Less fluid reaches the distal nephron, so overall fluid conservation is obtained.
The source for that is an editorial from 2004 that has some good other sources, including what appears to be the 1959 original paper finding this seemingly-paradoxical result.
Thiazide diuretics inhibit the NaCl co-transporter (NCC/TSC) in the renal distal convoluted tubule (DCT). The DCT is water impermeable and considered to be part of the diluting segment. Therefore, the water-preserving effect of thiazides is unlikely related to a direct effect on the DCT. In fact, the most widely accepted hypothesis suggests that the antidiuretic action of thiazides is secondary to increased renal sodium excretion. The renal sodium loss causes extracellular volume contraction leading to lowered GFR and increased proximal tubular sodium and water reabsorption. Hence, less water and solutes are delivered to the distal tubule and collecting duct and are lost as urine.