Wilkerson retired the first 17 batters he faced before allowing a sixth-inning single to pinch-hitter Jose Martinez. Randal Grichuk homered in the seventh for the only other hit off the right-hander.
Wilkerson struck out five and walked none in seven innings.
“I was pretty comfortable on the mound today. I think the pressure, or lack thereof, kind of took a lot of weight off my shoulders," said Wilkerson, a 28-year-old rookie. "It's almost surreal right now. I have the lineup card and all that stuff. It's kind of setting in now."