He shot 70 and Karlsson 69 in heavy rain which left them on 137, one shot ahead of the overnight leader Alexander Cejka, who, despite having dry weather for 17 holes, could manage only a 72.
"You just don't expect wet weather in Morocco and I didn't even bring a sweater," Torrance said. "But the conditions were horrific, very wet and freezing. I don't like wearing waterproofs and I played in my ordinary trousers for six holes but they got so wet I had to take them off.
"Fortunately there was a little tent between the sixth green and the seventh tee and I had a quick change. It wasn't a great day to play golf and you had to show great patience and resolve but I managed to keep my concentration."
Torrance did particularly well as he and Mark James played in a two-ball between a field of three-balls because their playing partner, Wayne Westner, of South Africa, was forced to pull out with a rib injury.
"It was terribly slow because we waited on almost every shot but you just have to get on with it," Torrance said after making four birdies.
He was especially pleased with the last two holes. "At the 17th I went over the back with a sand wedge into a terrible lie," he said. "But I chipped back to six feet and holed the putt for a par. Then I hit a two- iron and a seven-iron to 15 feet at the last and holed that for a birdie to share the lead."
MOROCCAN OPEN (Agadir): Leading second-round scores (GB and Irl unless stated): 137 R Karlsson (Swe) 68 69; S Torrance 67 70. 138 A Cejka (Ger) 66 72. 140 M James 70 70; M Mackenzie 68 72; G Levenson (SA) 69 71. 141 S Richardson 70 71; A Gillner (Swe) 68 73. 142 D Gilford 71 71; C Rocca (It) 72 70; A Coltart 70 72; I Spencer 72 70; D Carter 69 73; E Darcy 68 74. 143 P-U Johansson (Swe) 73 70; D Ray 71 72; M McLean 73 70; J Robinson 70 73; P Mitchell 71 72; P Affleck 73 70; M Besanceney (Fr) 68 75; A Hunter 75 68; P Price 71 72; J Hawkes (SA) 73 70; A Bossert (Switz) 69 74.