Number 10 Murphy combined with number nine Connor Sully for a 47-run partnership to guide Australia to their second victory of the group stage, enough to finish above England for second place in Group B.
Bowling first, England was dismissed for 252, with Murphy dismissing opener Jordan Cox for 25.
He finished with figures of 1/35 off his ten overs.
After a strong start which saw the Australian side at 3/153, the team suffered a middle order collapse to be 8/206 when Murphy made his way to the crease.
Murphy found the boundary twice in his ten balls as he and Sully took the side over the line, with Sully getting the final run on the last ball of the game.
In a post game interview, Murphy described the final moments of the game as some of the best of his career.
"It was incredible, we were down and out at one stage so to do that and get ourselves through to the quarter-finals was unbelievable, probably the best feeling I've had on the cricket field."
The win sees Australia advance to the quarter finals of the tournament.