The striker fired home the Shrews' third goal after 77 minute as they battled back from a 3-1 deficit in the friendly fixture to secure a 3-3 draw.
Asante's strike came after he caught Zat Knight in possession mid-way inside the Bolton half, before racing through on goal and calmly slotting the ball home.
Unfortunately for Asante, he also picked up a hamstring injury during the match and was substituted after 80 minutes.
“We’re fearful now that Akwasi has done a hamstring though. We hope it’s not too serious," said Shrews boss Graham Turner.
Blues face Shrewsbury
in a friendly fixture at the Greenhous Meadow Stadium on Tuesday evening.
Meanwhile, left-back Amari’i Bell’s Nuneaton Town were held to a goalless draw at home by Worcester City.