Gilford, who won this tournament last year, led for most of the day with a 68 and, with the wind showing no sign of relenting, was expected to stay in front as many scores went into the 80s.
However, Spence, 29, who loves playing in windy conditions, covered the first nine holes in a two- under-par 34, then took the lead with a birdie two at the 17th hole, where Gilford had earlier had an eagle.
'I hit a very low ball so the conditions suited my style,' said Spence, who, along with Gilford, was a member of England's winning team in the Dunhill Cup at St Andrews in October.
Gilford has made a good start to the year: joint sixth in Madeira, joint ninth in Dubai and joint 10th in Tenerife. Yesterday he began with three birdies and had two more, in addition to his eagle three. He also had three bogeys, taking three putts at the seventh, chipping a bad eight-iron to the 15th and hitting a tree at the last.
Gilford and Spence, who had only one bogey, at the ninth hole, were the only players to break 70.
Gilford's playing partners, Seve Ballesteros and Steven Richardson, both shot 73. Apart from the two leaders, the best scores were 70s from the South African Wayne Westner, Stephen Ames, from Trinidad and Tobago, and Miguel-Angel Martin, of Spain.
MOROCCAN OPEN Leading first-round scores (GB or Irl unless stated): 67 J Spence. 68 D Gilford. 70 W Westner (SA), S Ames (Trin), M- A Martin (Sp). 71 J Payne, M Poxon, E Darcy. 72 M Guzman (Arg), A Lebouc (Fr), S Grappasonni (It), J Townsend (US), O Sellberg (Swe), D Curry, A Gillner (Swe), M Mouland. 73 G Brand Jnr, S Field, M Farry (Fr), S Ballesteros (Sp), S Richardson, C Montgomerie, F Nobilo (NZ), R Mackenzie (Chile). 74 C McClellan (US), R McFarlane, A Sherborne, C Rocca (It), P McGinley, O Karlsson (Swe), R Drummond, D Ray, M McLean, S Torrance, A Binaghi (It), M James. 75 R Karlsson (Swe), M Sunesson (Swe) T Pernice (US), J Van De Velde (Fr), A Hunter, P Quirici (Swit), P Eales, R Chapman, I Palmer (SA), M Roe, K Waters, D Smyth, S Luna (Sp), D W Basson (SA). Selected: 76 J Parnevik (Swe), A Forsbrand (Swe), D A Russell. 77 W Riley (Aus), M Lanner (Swe), R Rafferty. Disqualified: H Selby-Green.