The stomach of actual species is already tolerant to low pH, as it has to handle gastric liquids. The intestine is not resistant to acids, and the content of the stomach is neutralized by basic substances which balance the pH.
A similar approach can be applied to your fictional species: basic solutions can be used to neutralize the pH of the ingested water, and the section from the mouth to the stomach can be covered with the same acid resistant mucus which covers the stomach. The resulting salts would have to be expelled by the body through urines or feces.
Another option would be for the species to swallow small limestone stones/cobbles together with the water. These (or similarly reactive elements) can also neutralize the pH. The produced gas would force your animal to burp some more. This can be a useful element for your plot (Tirannosaurus burpus...).
Limestone is mostly made up of the mineral calcium carbonate (CaCO3). This is not very soluble, so rocks don't dissolve very quickly. But if you add an acid, you add hydrogen ions (H+), which will react with the carbonate to form hydrogen carbonate HCO3- ions, which are very soluble in water, and the limestone will dissolve. Or, if there is more acid, two hydrogen ions will react with a carbonate to form carbonic acid - H2CO3 - which will decompose to form carbon dioxide - CO2 - which eventually bubbles off into the atmosphere, and water H2O.