No he didn't.
Its claimed that Mordred did. In the battle against Mordred Arthur ran Mordred through with his lance. Dying, Mordred gave Arthur a mortal wound to the head with his sword. Arthur killed Mordred.
Pellinore did in fact (according to those that believe) face Arthur in one to one combat. During this Arthur's sword snapped in two. This was NOT Excalibur buts its predecessor. Merlin, who was watching put Pellinore to sleep to prevent further injury. Merlin warned Arthur NOT to kill Pellinore as his sons would one day live to become 2 of Arthurs greatest allies against Mordred