New Barnsley head coach Jose Morais lost his first game in charge as Burton won 2-1 at Oakwell with first-half goals from Jamie Allen and Jacob Davenport.Barnsley applied strong pressure in the second half but they were restricted to a solitary goal, scored by Daniel Pinillos.The result ended Burton's run of seven games without a win and saw them climb off the bottom of the Sky Bet Championship, going above Barnsley.Allen struck inside the first minute, beating goalkeeper Nick Townsend with a fine effort from around 25 yards. It was Allen's first goal for Burton since arriving from Rochdale in the summer.Burton's record signing Liam Boyce, who was making his full debut for the club, then shot wide following a Davenport free-kick.Barnsley's Joe Williams put a long-range effort wide after receiving the ball from Oliver McBurnie.When Barnsley skipper Andy Yiadom crossed the ball into area, aiming for the head of Liam Lindsay, goalkeeper Stephen Bywater was alert to the danger, safely gathering the ball.There was a reprieve for the hosts when Hope Akpan handled the ball as he threatened to find a way through the centre of the Barnsley defence after being put through by Martin Samuelsen.Burton increased their lead in first-half stoppage time when Davenport floated his free-kick over the defensive wall and into the top left-hand corner of Townsend's net.Matt Mills had a shot blocked and Lucas Akins was forced to hack the ball clear in the box as Barnsley made a promising start to the second half.Bywater was then called into action, saving Adam Hammill's angled shot.At the other end, a Davenport free-kick was met by Samuelsen, who headed over.Barnsley striker Tom Bradshaw was pulled back as he threatened to break clear through the centre with Tom Naylor perhaps fortunate to escape with a yellow card.The resulting free-kick, taken by Gary Gardner, was well saved by Bywater, diving to his right.With Bywater off his line, Naylor then made a crucial block to divert McBurnie's goal-bound effort.Barnsley went close to scoring when Mamadou Thiam's corner was met by Mills whose header hit the bar.The pressure applied by the home side paid off in the 75th minute when Yiadom played the ball to Pinillos whose low and driven effort beat Bywater with the aid of a deflection.Barnsley continued to press late on and had the ball in the net in stoppage time, but the effort was ruled out. They have now won just once in their last 18 outings and are without a win in seven games.