Also missing the cut was defending champion Michael Hoey of Northern Ireland who signed for a third round 72 for a two-under tally.
Grace set the European Tour alight this year in winning three events in 11 appearances and arrived in Scotland after having captured a Sunshine Tour last week in Fancourt.
And Grace's efforts this year have been so amazing Els had no hesitation in declaring he could win the Open Championship which Els won in 2002 and again this year at Royal Lytham and St Annes.
"His game is so good Branden could well enough win an Open Championship," said Els.
The current world No 49 is a graduate from the Ernie Els Foundation which the four-time major winner established in 1999 to help assist talented South African golfers.
Els got his first real sight of Grace's prowess in capturing the 2007 South African Open at Port Elizabeth.
"Branden has always been a quality player, and he's really come on now," said Els.
Top scores
196: Branden Grace (SA) 60 67 69
200: Thorbjorn Olesen (DEN) 63 69 68
201: Alexander Noren (SWE) 64 72 65, Fredrik Andersson Hed (Swe) 64 71 66
Also
211: Michael Campbell (NZL) 67 71 73.
- AAP