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.
1. Illan Meslier - 6
Made some smart saves, distribution wasn't great, some good balls to Ayling before playing it out became more problematic
2. Luke Ayling - 6
Struggled with Kyle Walker-Peters in the second half having done well in the first half. Got forward to good effect though and kept going.
3. Stuart Dallas - 6
Better in the second half as the game went on, than in the first when Livramento caused issues. Started to have more influence later on.
4. Liam Cooper - 7
Not flawless on his return but solid. Read the game well in the main, made interceptions, made life tough for Saints attackers in the air.
5. Diego Llorente - 6
Brought an element of drama at times that felt unnecessary, some mixed moments of defending and in possession.
6. Adam Forshaw - 6
Couldn't give Leeds the control they needed but was fully committed, crunched into tackles, some clever passing.