Markus Schopp recorded his first win as Barnsley head coach after Dominik Frieser's first-half goal gave them a 1-0 victory at home to Coventry.
Coventry had a number of good chances to equalise, including a stoppage-time penalty which Viktor Gyokeres failed to convert, as the Tykes held on.
Barnsley were strong in the opening exchanges, but Coventry responded with Gyokeres setting up Callum O'Hare who shot just wide.
O'Hare was then involved in the build-up which saw Coventry threaten again, setting Ian Maatsen free down the left and his cross just evaded Tyler Walker.
Taylor suffered a shoulder injury soon afterwards and had to be replaced in the 17th minute, making way for Martyn Waghorn.
The visitors went close in the 20th minute when Gustavo Hamer's free-kick picked out Kyle McFadzean, whose header went over the bar.
As Coventry continued to press, they hit the woodwork in the 26th minute. Ben Sheaf found Maatsen out wide and his ball into the area was met by Gyokeres, whose volley came back off the bar.
The hosts also made an enforced substitution with Carlton Morris going off to be replaced by Clarke Oduor.
Barnsley took the lead in the 39th minute, with Frieser finding the net with a shot from the right-hand side of the area after receiving the ball from Romal Palmer.
An effort from Michal Helik early in the second half went over following a corner and the hosts threatened again soon afterwards when Cauley Woodrow put a glancing header wide.
Coventry nearly equalised shortly before the hour-mark when Maatsen's corner found Michael Rose, whose header was cleared off the line by Woodrow.
Waghorn also put a header wide from O'Hare's cross.
The visitors went close again when Hamer's free-kick was well saved by Brad Collins, and another effort from the Sky Blues saw Hamer's shot from distance go over.
Jake Clarke-Salter came to Coventry's rescue when he made a great challenge to dispossess Odour in a dangerous position.
Coventry then won a penalty in stoppage time when Jamie Allen was brought down inside the area but Gyokeres' effort from the spot was saved by Collins.
