Captain Cooper started against the Saints and was solid defensively as his side dominated most of the first half and took a deserved lead through Jack Harrison.
Southampton worked their way back into the game in the latter stages of the first half and then came out flying following the interval, a sublime James Ward-Prowse free-kick levelling matters.
Both sides had chances to win it, Leeds recovering from their poor start to the second half as Phillips came off the bench to calm the home side down but there was to be no victor and the spoils were shared.
Leeds are now unbeaten in three and sit eight points clear of the drop zone thanks to Watford's 2-0 defeat by Liverpool earlier in the day.
13. Kalvin Phillips - 7
Calmed everything down. Started to help dictate the play and move Leeds forward from deep. A few signs of rust here and there.
14. Pascal Struijk - NA
On in the very final minutes to replace Ayling and ended up doing some important defensive work as Saints pressed for a winner.
15. Anthony Taylor - 8
Refereed it sensibly for the vast majority, ignored theatrics and pressure being put on him by both sides, got the big things right.