Paul Lawrie and Stephen Gallacher got the first point on the board in the day’s opening four-ball with a 3&2 win against Thomas Bjorn and Miguel Angel Jimenez.
Europe immediately levelled before the third match was halved.
But two victories, including a comprehensive 5&3 from final pair Nicolas Colsaerts and Gonzalo Fernandez-Castano, earned Jose Maria Olazabal’s side a 3.5-1.5 lead going into today’s four-balls.
But Torrance said: “They played very well. Our boys played very well too, but they made a few more birdies than us.
“Our turn on day two.”