Teenager Ben Sahar, on loan from Chelsea, grabbed his first league goal in the 18th minute before Ben Watson pulled one back for Palace. Midfielder Wade Small eased Wednesday in front again before Lawrence had the final word seconds before full-time.
Palace, unbeaten in five games, almost snatched the lead in the sixth minute when Wednesday failed to cut out a Tom Soares cross from the right flank. Clinton Morrison's spectacular shot on the turn beat Lee Grant only for the ball to crash against the bar.
The woodwork foiled Wednesday minutes later when a poor clearance fell to the lurking Sean McAllister whose left-foot strike from almost 30 yards hit the angle.
Midfielder Soares squandered an opportunity to open the scoring when he failed to connect with Morrison's low cross before Wednesday broke the deadlock, Sahar and Deon Burton exchanging passes before the teenager coolly slotted the ball beyond Julian Speroni's reach.
Palace were almost level two minutes later, full-back Clint Hill flinging himself at Watson's corner as Grant pulled off an eye-catching one-handed save as he palmed away the header.
The London side were back on level terms in the 40th minute, Watson hitting a stunning goal curling his 28-yard free-kick into the top left-hand corner.
Sahar almost grabbed a second goal minutes after the re-start but his stinging 20-yard drive hit Speroni's shoulder.
Veteran midfielder Graham Kavanagh was twice foiled by the Palace keeper before Small struck in the 68th minute, running on to Burton's pass before cutting inside and slipping the ball wide of the advancing Speroni.
With the seconds ticking away Palace piled on the pressure and Lawrence stabbed the ball home from close range.