Díaz hit his first major league homer, a pinch-hit shot to start the fifth inning.
Thompson (1-1) started the planned bullpen game and limited Atlanta to three hits, striking out six in a longer-than-expected outing. The 27-year-old right-hander pumped his fist after his outing-ending strike out of Ronald Acuña in the fifth.
In addition to the win, Thompson got his first major league hit when he singled in the second.
Freddie Freeman hit his 15th homer, a two-run shot against reliever Anthony Bass in the eighth, as the Braves lost their fourth straight.