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The visitors took the lead when James Morrison fired past Joe Hart in the 11th minute. The West Bromwich Albion midfielder was allowed too much time on the edge of the area, although questions will be raised of the goalkeeper.
It stayed until half time, although Wayne Rooney may feel aggrieved with an offside decision that went against him just before the whistle.
The Scots soon retook after the restart thanks to Kenny Miller, who received the ball with his back to goal and, after making a yard of space, fired low beyond Hart.
Southampton striker Rickie Lambert came on to win his first England cap, replacing Wayne Rooney in the 68th minute. His introduction could not have gone much better, as he headed home from a corner with his first touch in international football.