The Taranger (Master Sverre Solberg) had been escorted by British aircraft after leaving Liverpool, which attacked an U-boat contact on 30 April at about 8°W. U-95 spotted the unescorted ship in AL 3178 at 06.20 hours on 2 May and began to chase her, but course changes and the high speed of the ship prevented any attacks until a torpedo was fired at 02.08 hours on 3 May, but it became a surface-runner. At 02.45 hours, the U-boat attempted to stop the vessel with MG fire about 150 miles southwest of Reykjavik, but the ship (armed with two Hotchkiss MG) tried to escape zigzagging at full speed and sent emergency messages so the Germans opened fire with the deck gun after 10 minutes and scored 16 hits with 21 rounds. After the first hits, the engines were stopped and the crew began to abandon ship while the shelling continued from the starboard side. The port lifeboat got clear, but before the starboard boat could be launched the master was killed and three crew members were wounded. The U-boat went to the other side and fired at torpedo at 03.12 hours which again became a surface-runner and a dud. At 03.16 hours, the stern torpedo was fired that hit underneath the bridge and the ship broke in two and sank after being hit by a second coup de grâce at 03.25 hours.

Alerted by her radio calls, HMS Echo (H 23) (LtCdr C.H.deB. Newby, RN) was sent out, but after a fruitless search for 8 hours she headed for Iceland. Both lifeboats set sail for Iceland, but the starboard boat lagged behind. The next day, its occupants spotted convoy OB-320, were picked up by HMS Begonia (K 66) (Lt T.A.R. Muir, RNR) and landed at Reykjavik on 10 May. On 5 May, the seriously injured first engineer had been transferred to HMS Wolverine (D 78) (LtCdr J.M. Rowland, RN) which had a doctor on board. In the morning on 5 May, the 17 men in the port boat saw land and were shortly thereafter rescued by the Icelandic motor fishing vessel Sigurfari (MB 95) (Skipper Bersør Guojønsson) about 46 miles from the coast. The vessel took the lifeboat in tow for Akranesi from where they were taken by passenger vessel to Reykjavik on 6 May.