The Scotsman took just an hour and 47 minutes to vanquish Kokkinakis, fueling speculation he will partner his brother Jamie in Saturday’s doubles rubber against Lleyton Hewitt and Sam Groth.
Bernard Tomic made the most of his return from a Tennis Australia suspension that saw him miss the quarter-final, scoring a hard-fought 6-3 7-6 (7-2) 6-7 (4-7) 6-4 victory over Dan Evans to level the tie at 1-1.
"It isn't my decision, it's up to the captain to decide that but I now have the option to be picked because this match was quick," Murray said of his prospects of playing on Saturday.
"I think everyone in the team wants to play, everyone wants to try to help where they can.
"The players have a job to do, but we don’t make the decisions."
A shell-shocked Kokkinakis admits he simply had no answer for Murray.
"That's the best he’s ever played against me. I just got killed," he said.
Controversial Aussie Nick Kyrgios was not selected for the tie after a tumultuous few weeks following his 'Kokkinakis banged your girlfriend' sledge to Stan Wawrinka.