Current world champion Wilson displayed impressive form early on, wrapping up the first frame with a break of 71 and racing to an early 3-1 lead.
Brecel, the 2023 World Champion, fought back valiantly, but Wilson's clinical play and a crucial missed opportunity for Brecel in the sixth frame proved decisive.
The final frames were a rollercoaster of emotions. Brecel fought back with a series of impressive breaks, while Wilson showcased his fighting spirit and composure.
A grippingly suspenseful ninth frame ultimately went on for 30 minutes as balls began to flow erraticaly, but was eventually won by Brecel after more than 30 minutes to leave the Belgian fighting to the end at 5-4.
The final frame was a an even more tense affair, with both players facing pressure.
Ultimately, Wilson held his nerve to sink a long pink, securing the victory and booking his place in the semi-finals against Judd Trump, who defeated Ding Junhui 6-3 earlier in the day.
"To be honest, with what's gone on today, that's one of the best wins of my career," Wilson told Eurosport after the victory,
"I'm in bits after that, honestly.
"It's up to me and Judd now to give them (the fans) value for money. Hopefully, we can deliver tomorrow night, and everybody goes home happy."