A little past midnight on a recent Friday, Manuel López, a 26-year-old lawyer, accidentally drives his beige Volkswagen Polo into a gun battle between rival drug gangs in the tourist resort of Acapulco. As bullets tear into his car, he hits the brakes and tries to run. He makes it less than a yard before falling dead.

Mr. López is the first victim of July 29, a hot summer day much like any other in Mexico's battle against powerful drug-trafficking gangs. Over the next 24 hours,...