Djokovic cruised through the first set as he stormed to a 6-2 win.
But while on serve in the second the world No 1 had a problem with his equipment.
Bautista Agut earned the first break in the second set to lead 2-1 but at deuce Djokovic had to change his racket because of a broken string.
Then while the Serbian was on serve two games later another racket string snapped after sending a delivery to his opponent.
Although there is no clear worry on Djokovic’s face, there must be a slight concern in the back of his mind about a further racket string possibly breaking at a crucial point of the match.
Djokovic went on to lose the second set 6-4 as the pair headed into the third on level terms.
Speaking ahead of the tie, Djokovic knew he would be in for a tough afternoon against an opponent who has already beaten him twice this season.
“His consistency, I think. His ability to stay in the point even when it seems like he’s on the back foot,” Djokovic said.
“He’s got amazing consistency I think with his shots. Very flat from both forehand and backhand.
“He has improved his backhand. I think he’s got more depth on his backhand.
“The ball bounces lower on the grass, which is I think more suitable to his style of the game. He doesn’t like when the ball bounces higher to his backhand.
“He’s been definitely playing some very, very high-quality tennis in this tournament.
“He has won twice against me so far this year. That’s certainly going to give him confidence coming into the match.
“Obviously playing on grass, it’s different. Semifinals of Grand Slam, going to try to use my experience in being in these kind of matches, get myself tactically prepared.
“Hopefully I can execute everything I intend to do.”