Both sides had records to put straight – Cardiff had not beaten the Royals in their last nine clashes in all competitions, while Reading arrived having won just one of their last nine away league matches in the Welsh capital.
Cardiff boss Neil Harris gave left-back Greg Cunningham his first start for the Bluebirds since January 2019, when they were in the Premier League, and also drafted Wales international Will Vaulks into the midfield.
Paunovic made one change from the team that had beaten Barnsley, bringing goalscorer Yahou Meite into the starting line-up.
It was the specialist long throws from Vaulks that caused the biggest problems for Reading in the early stages, while a long ball from half-way by skipper Liam Moore allowed Meite to use his pace to nip in between two defenders and force Alex Smithies into the first save of the game.
The visitors came on strong in the final 10 minutes of the opening half and Lucas Joao headed just wide from a corner swung in from the left, and then twisted and turned on the edge of the area before firing a left-footed shot that forced Smithies to dive full length.
Having taken the upper hand at the end of the first half, Reading maintained their pressure and hit the front within 70 seconds of the restart.
Olise swung in a free-kick from the left and centre-back Michael Morrison met it perfectly on the edge of the six-yard box to head home.
Cardiff responded with their best move of the game, with Osei-Tutu and Marlon Pack setting up Vaulks for a shot from the edge of the area that whistled past the left hand upright.
Lee Tomlin replaced Vaulks just after the hour and, with virtually his first touch, fired in a shot that cannoned off the goalscorer Morrison and forces Rafael to save acrobatically with his feet.
Reading then killed the game off with a second goal a few minutes later when Josh Laurent played in the dangerous Joao, who held off Nelson, twisted onto his left foot and fired home from near the penalty spot.
Tomlin grabbed a consolation goal for the Bluebirds nine minutes from time when he prodded into the net after a Kieffer Moore header from a corner.