Lee Johnson's first game as manager at Oakwell ended in a fourth successive win and clean sheet as Barnsley beat Coventry City 1-0.
George Waring got his second goal in as many games to lift the Reds up to tenth in League One, two points off the play-off places and 12 clear of the relegation zone.
Johnson kept the same team that won at Gillingham on Saturday while Dale Jennings, Sam Winnall and Jean Yves M'voto came back onto the bench for Kane Hemmings, George Williams and Leroy Lita, who has been sent out on loan to Notts County.
Goalkeeper Adam Davies almost gifted the visitors the lead in the fourth minute when his attempted clearance was charged down by Dominic Samuel and the ball flew just wide.
Barnsley captain Martin Cranie then put a header just wide against his old club before ex-Red Marcus Tudgay hit the right post with a low 20-yard effort.
After Waring and Odelusi both went close with headers early in the second half, the Barnsley striker put them ahead on 57 minutes. Waring, on loan from Stoke, met Conor Hourihane's right-wing free-kick with a diving header and found the back of the net from seven yards out.
Former Barnsley man Frank Nouble came on as a substitute and fired across the face of goal then later appealed for a penalty after a challenge by Mason Holgate.
Coventry almost levelled in injury-time when Matthew Pennington's volley was cleared off the line by Ben Pearson.
