U23s chalk their first point on the board in the Premier League Cup, despite having ten-men for over an hour of the match.
Jordan Cropper was shown a red card for blocking the ball on the line with his arm with just 35 minutes played.
However, Rafael Camacho could only strike the penalty wide of the post.
And the Clarets then took the lead through Tinashe Chakwana just 10 minutes into the second half.
Liverpool then equalised just moments later through Glen McAuley.
The hosts were then awarded a second penalty of the match with 10 minutes to go, however, Adam Legzdins denied Adekanye, to continue his fine run of form completing three penalty saves out of his last four.
The Reds started brightly and came close through Adam Lewis, as the midfielder’s strike sailed just over Adam Legzdins’ crossbar.
Liverpool then had a great opportunity to break the deadlock, as the ball fell to Nico williams at the back post.
However, the full-back’s close range effort was denied terrifically by a sliding Oliver Younger.
The Clarets’ first real chance came through Dwight McNeil, as the winger fired the ball just wide of the post following a good build-up.
The hosts were then awarded a penalty with 35 minutes played, as Cropper’s effort to block the ball on the line was adjudged to of come off the defenders arm.
Resulting in the Burnley man being shown a red card.
However, Rafael Camacho stepped up to the spot and struck the ball just wide of the post.
Olatunde Bayode then came close to putting the Clarets ahead, as his first-time hit fizzed just wide of the side netting.
Burnley came out the blocks raring to go in the second half and got their reward.
Dan Agyei burst forward towards goal, before striking straight at Grabara, who could only parry the effort into the feet of Chakwana, who slammed home the rebound.
However, the visitors were not ahead for long, as Glen McAuley nodded in Camacho's cross from the left.
The Clarets came close to regaining the lead 10 minutes later, as the ball fell to Chakwana, who could only blaze the ball over from a god position.
As the home side began to pile late pressure on, they were awarded a second penalty of the afternoon.
Bobby Adekanye stepped up this time and Legzdins got down low to deny the winger from the spot and keep the scores level.
And with seconds to go, up stepped Legzdins again, as the Burnley keeper' pulled off an excellent double save to deny McAuley twice from yards out.
BURNLEY: Legzdins, Cropper, Younger, Glennon, Koiki, Bayode (Blair 77), McNeil, Howarth (Clarke 37), Benson, Chakwana, Agyei (Harker 81).
Unused; Bruce, Cook.