After a goalless first hour, there were seven goals in an extraordinary conclusion to the contest.
Gabriel Osho put the visitors ahead, but Hepburn-Murphy equalised immediately and Easah Suliman headed the hosts in front before Tom McIntyre made it 2-2.
Corey Blackett-Taylor restored Villa's lead only for Teddy Howe to level with nine minutes remaining.
But Hepburn-Murphy (pictured), a nominee for April's PL2 Player of the Month and the two-goal hero in their Premier League Cup semi-final win over Leicester City, had the final say seconds before the tie would have gone to extra-time.
Villa, who finished second in the table, now play third-placed Brighton & Hove Albion at Villa Park in the final, with the winner getting promoted to Division 1.
Aston Villa: 4 May v Swansea (A) PL Cup