The Manchester United youngster fired home from inside the box to sink a spirited Moldova side, who finished with 10 men after the sending-off of Constantin Bogdan.
The home side dominated after Lawrence's early opener and had plenty of chances to increased their lead with Billy Bodin firing just wide and a Lawrence seeing a free-kick punched clear.
After the break substitute Robert Ogleby put the ball in the net after Lee Lucas had struck the woodwork, only for his effort to be ruled out for offside.
Bogdan was dismissed for a second heavy challenge in the 72nd minute and Wales coasted to a victory that delighted coach Geraint Williams.
Williams told the Football Association of Wales' official website: "It was important to get the group off to a winning start and on another night we could have had three or four."
- Sports & Recreation