Iran's Vafaei made four half-centuries and a century to secure his victory against a disappointing Murphy.
The 2008 winner, who is ranked seventh in the world, struggled to find his rhythm and top scored with a 64 break.
Matthew Selt defeated fellow Englishman Ali Carter 6-3 in Sunday evening's other match and will face Vafaei next.
Like Vafaei, Selt came through qualifying to reach this stage of the competition and settled into his contest with Carter with two superb breaks of 111 and 102 to head into the interval level at 2-2.
The players then traded frames but Selt took a hard-fought seventh frame and reeled off the next two to advance.