After placing forward Arthur Kaliyev on injured reserve last week, Byfield was promoted from the Kings' AHL affiliate, the Ontario Reign.
The 20-year-old – who was the No. 2 overall pick for the Kings in the 2020 draft – claimed an assist in Tuesday's contest at Crypto.com Arena, with goals on the night coming from forwards Rasmus Kupari, Anze Kopitar and Adrian Kempe.
Speaking after the win, McLellan outlined his admiration for Byfield's all-round performance, saying: "I thought he had a tremendous game. He's always been fast and quick, but he really used his body to his advantage.
"He stripped pucks, he created and loosened up pucks for his linemates, backchecking, he caught people from behind, he was responsible defensively and he set up a number of offensive plays.
"To me, that was as good a game as we've seen from Q all year and he had some good ones at the beginning. Real positive sign for him."
Although beaten twice in the contest, first by Miro Heiskanen and then Jason Robertson, Kings goaltender Pheonix Copley made 28 saves as his team produced their seventh win from their last nine games.
"The game as a whole was very competitive," McLellan said. "It was a hard, heavy, physical – not always big hits – but just the battles for loose pucks and for ice, it had a big forecheck component to it.
"That part of it and for us to play the way we did, a lot of things we had to fix from the last time we were in Dallas and I thought we accomplished some of that."
The Kings are now 22-13-6 for the season and sit second in the Pacific Division on 50 points, but their coach is only looking as far as the next game, which comes at home to the Boston Bruins on Friday before a trip to the Las Vegas Golden Knights on Sunday, who sit four points ahead of L.A.
"I think we can be [a 100 point team], we're working towards that, but our goal is to become a 52 point team," McLellan added.
"I know that's not what you want to hear but the team coming in here on Thursday, what are they shooting for, their 70th point, that's the type of challenge that we have.
"Then the next game after that, we've got to go into Las Vegas and play and then after that we have Edmonton coming in. So, this string of games right now, every night is a big battle and I think if we start thinking about big numbers and chunks, it's not going to do us any good. One at a time."