Torrance is two shots behind the Swedish leader, Robert Karlsson, in a tie for second place with Germany's Bernhard Langer and Constantino Rocca, of Italy.
Aged 39, Torrance believes he is still good enough to make the European Ryder Cup team again. He said: 'Ever since I first made the team in 1981 I seem to play better in the odd years. I don't know why, it's just worked out that way, but I definitely want to be in the team next year more than anything.'
Torrance is only 64th in the European money list and 30th in the Ryder Cup points table so he needs four good rounds in Stuttgart to boost his chances.
Despite having the worst of the weather, he used his putter to such good effect that he had seven birdies and not a single bogey on his card over the 6,839-yard, par 72 course.
Ignoring the rain that fell for most of his round, Torrance made a good start with a birdie at the first hole followed by a superb chip to save par at the second. He never looked back.
Another Scot, Sandy Lyle, had a good day after a sorry one-over-par 37 for the first nine, coming back in a six-under-par 30, which included six birdies.
The Yorkshireman Malcolm Mackenzie, who was joint fifth in the Open championship, and the Ryder Cup player, Paul Broadhurst, also shot 67 to boost the British presence on the leader board.
Karlsson, who was second to Nick Faldo in the European Open at Sunningdale recently, had seven birdies and an eagle in his 63 - his best score as a professional.
MERCEDES GERMAN MASTERS (Stuttgart): First-round scores (GB or Irl unless stated): 63 R Karlsson (Swe). 65 B Langer (Ger), C Rocca (It), S Torrance. 66 M Allen (US). 67 A Cejka (Ger), M Mackenzie, I Palmer (SA), R Davis (Aus), S Lyle, P Broadhurst, M A Jimenez (Sp), C O'Connor Jnr. 68 M Gates, S Ballesteros (Sp), I Woosnam, A Sorensen (Den), C Williams, R Rafferty. 69 A Murray, S McAllister, J Payne, D Cooper, C Moody, H Clark, F Nobilo (NZ). 70 D Silva (Por), A Sherborne, M Roe, G Levenson (SA), S Richardson, F Couples (US), E Darcy, P Walton. 71 J-M Canizares (Sp), J Hawkes (SA), R Claydon, P-U Johansson (Swe), D Gilford, J Rivero (Sp), P Mitchell, V Singh (Fiji), B Lane, J Spence, P Price, H Baiocchi (SA). 72 M Davis, S Luna (Sp), P Fowler (Aus), H Thul (Ger), S Struver (Ger), M Mouland, B Marchbank, E Giraud (Fr), P Senior (Aus), D Mijovic (Can), R Drummond, C Van de Velde (Neth), J Van de Velde (Fr), E Els (SA), P O'Malley (Aus), D Smyth. 73 M Poxon, R Lee, K Waters, E Romero (Arg), P Curry, P Hall, J Haeggman (Swe), T Giedeon (Ger), M Pinero (Sp), R Bernorst (Ger). 74 R Mund (Ger), J Parnevik (Swe), C Montgomerie,
J-M Olazabal (Sp), R McFarlane, J McHenry, M McNulty (Zim), G Turner, T Charnley, W Westner (SA). 75 C Mason, D Feherty, M McLean, A Binaghi (It), P Baker, P Way, P Teravainen (US), B Barnes, R Boxall, J Rystrom (Swe). 76 G Evans, M A Martin (Sp), G J Turner (NZ), D Randolff (Ger), D Williams. 77 O Sellberg (Swe), V Fernandez (Arg), D J Russell. 78 G Ralph, B Malley (US), T Goegele (Ger). 80 M Lanner (Swe). 81 T Jacklin.
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