The Kilkenny man survived with a shot to spare as Spain's Pablo Martin took the halfway lead to remain on track for back to back European Tour wins.
Martin, the only player to win European Tour titles as an amateur and a professional, won the Alfred Dunhill Championship on Sunday.
The Spaniard, 23, added a 68 to his opening 65 at Pearl Valley Golf Estates as Murphy posted a battling 69 to make the cut by a shot on level par.
It was a brave performance by the Kilkenny man, who looked likely to miss out for the second week in a row after taking a quintuple bogey 10 at the 13th in a first round 75.
Martin opened up a two shot lead over Denmark’s Anders Hansen (69) on 11 under par at halfway.
Michael Hoey was the best of the Irish in a share of 14th place on four under par after a second successive 70.
Damien McGrane (72) was a shot further back with Gareth Maybin following his 75 with a 68 to get to one under par.