"U" force sailed for France on 5 June, with Rich and her sister ship Bates in the screen of the bombardment group of Task Force 125 (TF 125), which consisted of the battleship Nevada and the cruisers USS Quincy, USS Tuscaloosa, and HMS Black Prince. From 6 June to 8 June, she screened the heavier units as they supplied gunfire support for the troops landed on Utah Beach to the northwest of the Carentan Estuary. On 6 June, Rich laid down a smoke screen which foiled an attack by German S-Boats.
Soon after 08:45 on 8 June, she was ordered by the Commander of Task Group 125.8 (TG 125.8) aboard Tuscaloosa to Fire Support Area 3 to assist the destroyer Glennon which had struck a mine northwest of the Saint-Marcouf Islands. Rich proceeded at full speed to the area, and then followed in the wake of two minesweepers to the immediate area of the Glennon. Closing Glennon, Rich dispatched a whaleboat, only to learn that her assistance was not needed at that point. Rich then started to round the disabled ship and take up station ahead of the minesweeper which had taken Glennon in tow. She moved at slow speed, with extra hands on the lookout for enemy planes and mines.
At approximately 09:20, when Rich was about 300 yards (300 m) from the minesweeper Staff, which was in the process of taking Glennon in tow, a mine exploded 50 yards (50 m) off Rich's starboard beam. This tripped circuit breakers, knocked out the ship's lighting, shook up the ship hard, and knocked sailors off their feet, but caused no structural damage. Within a minute, the engine room reported that they were "ready to answer all bells". Three minutes later, a second mine went off directly under the ship. Approximately 50 feet (15 m) of her stern was blown off, from frame 130 aft, just aft of the 1.1-inch (28 mm) mount in 'X' position. Even though the blown-off stern section caught fire, survivors clung to her wreckage, and it sank shortly afterward. There was a three-foot sag in the main deck, and two torpedoes ran hot in their tubes. A third mine, another influence mine, exploded below the ice machine room forward, delivering the final blow 2 minutes later. The forward section was totally wrecked, the flying bridge demolished, and forward fire room severely damaged, and the mast came crashing down. Life rafts were ordered cut loose, and Rich was ordered abandoned. Several PT boats in a squadron commanded by LCDR John D. Bulkeley came alongside Rich to take off personnel. All this time, they were being shelled by German shore batteries. A few minutes later, she sank in about 40 feet (12 m) of water.
Of her crew, 27 were killed, 73 wounded, and 62 missing; in all, 91 were killed outright or died of wounds following their rescue. Rich was the only American destroyer escort lost in the invasion force. LCDR Michel, who suffered a broken leg, was awarded the Navy Cross for extraordinary heroism in the incident.