Dissonance grabbed all of the ones I could think of offhand. A few additional ones not mentioned though include:
During the 1956 Suez Conflict: The Royal Navy CL HMS Newfoundland engaged the Egyptian Navy frigate Domiat, a former RN River-class frigate, in a nighttime gun battle. The Domiat was rapidly set on fire, and then sunk by the RN DD Diana.
Also in this conflict, the Egyptian DD Ibrahim El Awal, a former RN Hunt-class destroyer, was engaged by the Israeli Navy destroyers Eilat and Yaffo after having shelled Haifa. The INS vessels, with help from airstrikes, disabled the Ibrahim El Awal, which then surrendered. It was incorporated into the Israeli Navy as INS Haifa, where it served until some time in the 1970s.
Going half the world away to Vietnam, the U.S. Navy and North Vietnamese fought several skirmishes during their long conflict. The Gulf of Tonkin incident is the most famous, but another interesting battle is the Battle of Dong Hoi. In this battle NVN torpedo boats and NVAF Mig-17s engaged a USN surface group that was trying to interdict nearby roads with naval gunfire. The USN responded with SAMs and gunfire. According to the wiki, it’s notable because it’s the first time that the USN came under enemy air attack since WW2, and got bombed. (Evidently the North Korean Air Force was unable to attack the USN during the Korean War.) The USN DD Higbee was hit squarely by a 250-lb bomb on the destroyer’s rear 5-in gun mount. Fortunately for the Americans, the mount had been evacuated shortly before, due to a hangfire in the gun. The Higbee withdrew, as did the rest of the group, and were promptly attacked by NVN torpedo boats. Two of those were sunk by USN gunfire.
While there were a multitude of NVN sampans, junks, and other small vessels sunk during operations like Operation Sea Dragon, I don’t believe the NVN lost any warships. Any resistance was provided by shore batteries, which accounted for a few hits on various UN vessels, but no sinkings. This page is a brief compilation of accounts during Sea Dragon.
Finally, in a nearby part of the world, the People’s Republic of China and the Socialist Republic of Vietnam fought a brief naval battle over the Spratly Islands in 1988. The Vietnamese were driven off a reef they’d occupied, at the loss of two “armed transporters” like this, and a heavily damaged landing craft, which looks to my untrained eye like an LST.
Some of the above strain the definition of “sunk warship”, but I think the various 1956 naval clashes count.