Lackey (6-5) yielded one run on six hits, walking one and striking out six in stretching his personal unbeaten streak to six starts.
With the game scoreless in the fourth inning, the Red Sox put David Ortiz, Mike Napoli and Jarrod Saltalamacchia aboard with two outs and Snyder belted a pitch that hit high off the left field wall, scoring all three runners.
Julio Iglesias later added a run-scoring single as the American League East-leading Red Sox took the opener of a three-game interleague set.
Rookie Robbie Erlin (1-1) absorbed his first major league defeat in his third career start for the Padres, surrendering three runs on five hits over 3 2/3 innings.
Jesus Guzman socked a solo homer for San Diego.