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Grace, who won for the fifth time on tour this year, closed with a two-under 70 over the Old Course, with the fast-rising Olesen coming in with a 68.
The 24-year-old began the week with a European Tour record-equalling 60 at the Kingsbarns course - the European Tour's pro-celebrity event is staged over three links courses - and was never overtaken after that.
Olesen did make a move in the final round, drawing level with seven holes to go, but the South African birdied the next three holes and with another on the last finished with a tournament record-equalling 22-under-par total.
Alone in third place, four strokes off the pace was Alexander Noren of Sweden, while another Swede, Joel Sjoholm, was fourth a further two strokes back.
Scotland's Stephen Gallacher, winner in 2004, finished in a tie for fifth after incurring a two-stroke penalty for playing the wrong ball at the 16th.
Scores from the European Tour Dunhill Links Championship at the par-72 course on Sunday at St Andrews:
266 Branden Grace (South Africa) 60 67 69 70 268 Thorbjorn Olesen (Denmark) 63 69 68 68 270 Alexander Noren (Sweden) 64 72 65 69 272 Joel Sjoeholm (Sweden) 65 67 70 70 273 George Coetzee (South Africa) 71 72 68 62
Lee Slattery (Britain) 67 70 68 68
Raphael Jacquelin (France) 69 67 68 69
Victor Dubuisson (France) 62 73 70 68
Danny Willett (Britain) 66 69 68 70
Stephen Gallacher (Britain) 67 70 65 71
Fredrik Andersson Hed (Sweden) 64 71 66 72 274 Steve Webster (Britain) 70 72 68 64 275 Magnus Carlsson (Sweden) 66 68 73 68
Ricardo Gonzalez (Argentina) 71 72 63 69 276 David Drysdale (Britain) 66 72 70 68
Oliver Fisher (Britain) 66 74 67 69
Chris Wood (Britain) 69 70 68 69
Anton Haig (South Africa) 65 68 73 70
Mark Foster (Britain) 72 69 66 69
Graeme Storm (Britain) 68 66 72 70
Thongchai Jaidee (Thailand) 65 71 67 73 277 Edoardo Molinari (Italy) 71 68 70 68
Mikko Ilonen (Finland) 72 71 66 68
Ross Fisher (Britain) 70 69 69 69
Brett Rumford (Australia) 71 70 69 67
Thomas Aiken (South Africa) 72 68 67 70
James Morrison (Britain) 70 69 71 67
Ashley Hall (Australia) 64 73 69 71 278 Darren Fichardt (South Africa) 71 66 72 69
Gonzalo Fernandez-Castano (Spain) 70 69 70 69
Padraig Harrington (Ireland) 71 73 66 68
Emiliano Grillo (Argentina) 70 69 67 72
Paul Waring (Britain) 69 66 70 73 279 Mathias Groenberg (Sweden) 74 66 69 70
Marc Warren (Britain) 70 70 69 70
Shane Lowry (Ireland) 69 69 71 70
Lorenzo Gagli (Italy) 69 67 72 71
Bradley Dredge (Britain) 69 69 72 69
Ernie Els (South Africa) 73 70 65 71
David Howell (Britain) 71 72 67 69
Oliver Wilson (Britain) 67 71 69 72
Maarten Lafeber (Netherlands) 71 71 65 72
Scott Jamieson (Britain) 68 74 68 69
Martin Kaymer (Germany) 70 71 69 69
Alejandro Canizares (Spain) 66 70 71 72
Peter Hanson (Sweden) 72 70 69 68 280 Anders Hansen (Denmark) 70 69 70 71
Dustin Johnson (U.S.) 72 71 67 70
Richard Johnson (Sweden) 71 69 70 70
James Kingston (South Africa) 68 69 70 73
Peter Lawrie (Ireland) 70 72 68 70
Matthew Baldwin (Britain) 69 69 72 70
Joost Luiten (Netherlands) 68 72 71 69
Michael Campbell (New Zealand) 67 71 73 69 281 Graham DeLaet (Canada) 71 69 69 72
Phillip Price (Britain) 71 67 69 74
Richard Finch (Britain) 69 72 69 71
Colin Montgomerie (Britain) 71 70 69 71
Jaco Van Zyl (South Africa) 72 69 70 70
Tommy Fleetwood (Britain) 66 73 72 70 282 Robert Rock (Britain) 71 72 66 73
Tjaart Van der Walt (South Africa) 72 70 69 71 283 Simon Khan (Britain) 68 69 70 76
Pablo Martin (Spain) 67 70 74 72
Soren Kjeldsen (Denmark) 69 73 69 72 284 Pat Perez (U.S.) 72 70 69 73
Charl Schwartzel (South Africa) 75 70 66 73 285 Rikard Karlberg (Sweden) 67 73 70 75 287 Fabrizio Zanotti (Paraguay) 68 66 76 77
