The 17 year-old created the opener for Beto before Iliman Ndiaye scored from the spot late on for the 2-0 win.
“I thought he was brilliant,” remarked Baines, who added: “It’s a great moment for us as a football club and for the coaches who’ve worked with Harrison through the Academy.
“To see him getting this exposure to the first team is why we all go to work. It’s brilliant to see that and I thought his performance was really good today.”
Baines stepped in after the dismissal of manager Sean Dyche and he also said: “The manager’s had to leave, and that’s not what anyone wants.
“There’ll be a new manager coming in – and that brings opportunity.
“It was a difficult day. But I think within all of that, there’s definitely now got to be hope and optimism. That’s something we’ve spoken about today. Things are changing: the Football Club, the ownership, the stadium, and things are being talked about."