The Scot had to sink a vital 10-foot putt at the third to ensure he halved the hole, before chipping in at the fourth to take the lead.
Lawrie's approach to the fifth green was spectacular, leaving him with another 10-footer for an eagle.
He sank it to extend his lead to two, before another birdie at the ninth gave him a commanding lead at the turn.
Snedeker was uncharacteriscally struggling with the putter, while Lawrie seemed to hole everything that was put in front of him.
Lawrie then proceeded to win the next three holes to establish a five-hole lead. He had a putt for a half at the 14th, which would have won the match, but it just slipped by the hole.