The 18-year-old hot prospect marked his first senior start with an eye-catching display against a seasoned Sheffield United side in Thursday's Carabao Cup win.
Robust youngster Cleary, who last week signed a first professional contract, looked after himself and the ball against a physical Blades backline and had a couple of efforts on goal.
Bruce admitted the youth team star had a 'pleasant surprise' when receiving his Cup starters orders on Wednesday.
"He's physical, powerful for a young boy," said boss Bruce. "He's still got a long way to go, don't get me wrong, but he wants to score a goal.
"He's got that mentality, it doesn't change, you can see that as soon as he comes into the team.
"He come in on his right foot and smashed one (at the keeper). He had a big chance, he won't sleep tonight.
"I was pleased for him, he got a bit of a pleasant surprise yesterday when he was told he was in the team. I'm sure he didn't sleep much last night.
"He can be very, very proud of himself, and can his family."
Bruce added on Cleary, who as a scholar was linked with a host of European clubs: "He can score a goal and he was close today. He had his first shot going in there.
"It didn't really faze him, the kid, it's the start of hopefully a very decent career."
Last night's Cup progression was a proud occasion for the Baggies academy, with eight graduates involved in the matchday 20, including another first start – for left-back Zac Ashworth, 19.
"I think they've done well," Bruce said. "Gardner-Hickman's come through, Tom Fellows has come through.
"I'm like everybody, the way the academy is I think we've proved over the last two or three years we've been successful with it.
"Unfortunately we've lost too many, where the system fails us, but we keep producing one or two which is essential for the good of the club.
"For now, with myself, I'm always likely to put a young one in and I'm delighted to give him his debut."