Ricardo Fuller's 15th goal of the season cancelled out Elliott Ward's first-half opener as both teams netted from the penalty spot, before Lawrence scored with 11 minutes left.
Coventry started this match which manager Chris Coleman described as "monster" in positive mood by attacking Stoke from the start.
Jay Tabb's floated cross from the left was met by a glancing header from Kevin Thornton which crashed against the bar in the third minute.
In the next attack, Michael Doyle's low 20-yard shot flew across the face of the goal as Stoke were penned back in their own half.
Coleman's team were rewarded for their dominance by taking the lead on the half-hour mark.
Thornton was brought down inside the box in a goalmouth melee by Carl Dickinson and referee Uriah Rennie immediately pointed to the spot.
Ward's right-footed penalty beat keeper Carlo Nash, who dived the wrong way.
Tony Pulis' side might have equalised in the 50th minute when Fuller turned Ward to curl in a shot which Kasper Schmeichel palmed away.
The dangerous Fuller won the visitors a spot-kick four minutes later when he weaved past two Coventry players before he was fouled by skipper Stephen Hughes.
The Jamaican tucked his penalty into the corner of the net.
Soon after, Fuller's left-wing cross teed up Stephen Pearson, but the on-loan midfielder from Derby just failed to connect with the ball.
But Stoke grabbed a vital second goal in the 79th minute when Richard Cresswell's shot was saved by Schmeichel, but the rebound fell to Lawrence and the substitute hit the ball into an unguarded net.