Jack Bearne netted the only goal of the game inside the opening 10 minutes after fine approach play from Ben Woodburn.
"Burnley gave us a tough game, to be fair to them, and it was a great test for the boys," U23s boss Barry Lewtas told Liverpoolfc.com.
"They were tough and direct but we did well, and the boys knew we had been in a game when they came off the field.
"It was just what we needed and we gave some much-needed minutes to the likes of Morgan Boyes, Billy Koumetio, Jack Walls and Ben.
"It was great to get back to winning ways and I'm pleased for the boys."