Sheffield United reaction: Chris Wilder lauds potential of talented Tottenham Hotspur prospect
The on-loan Tottenham youngster fired home after 33 minutes at the Macron Stadium to seal a fourth successive victory in the Sky Bet Championship for the Blades and one that moved them up to third in the table.
Carter-Vickers' first senior goal also ended a run of 10 away defeats, dating back 40 years, at their Lancashire hosts and United boss Wilder was quick to praise the defender.
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Hide Ad"He was up against it," Wilder said. "That wasn't under 23 football he has played out there. It's real football and he can be delighted with his debut."
Despite their contrasting league positions - Bolton lie bottom of the standings - Wilder was relieved to walk away with all three points.
He added: "We are delighted with the result. It was a hard-fought game and the result could have gone either way, if I am honest.
"Bolton's start hasn't been great but the similarity from last year - us knowing a little bit about them and them knowing a little bit about us - brought the teams closer together in terms of performances.
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Hide Ad"And because they have got proud people on their staff and proud players, they weren't going to let us come in and take the three points easily. We had to work extremely hard and defend for our lives at times.
"This, in my opinion, is our best result, not the best performance, from our season so far."