It was a disaster for bottom of the table Bari, who missed a penalty, saw two men sent off and lost to an Antonio Candreva wonder-strike.
It was a bottom-of-the-table battle, as Parma lifted themselves with Thursday's scraped 1-0 win over Sampdoria, but Bari had one point from six rounds. Salvatore Masiello, Abdel Ghezzal, Nacho Castillo, Emmanuel Rivas, Jaime Romero and Vitalii Kutuzov were out of action for the home side. Alberto Paloschi and Daniele Galloppa didn't make the trip.
The Ducali had an outstanding record here, winning four of their last seven games away to Bari.
Hernan Crespo's header from a Marques cross was just over the bar, while at the other end Nico Pulzetti's screamer was plucked out of the air.
Caputo and Massimo Donati had long-range efforts well smothered, but it was Parma who took the lead with a wonder goal.
The long Marques cross came from the left and Crespo's dummy let it through for a sensational Antonio Candreva volley into the near top corner. It was a very tight angle, but he aimed that right-foot finish perfectly.
Caputo flashed another effort over the bar and Bari were awarded a penalty when Massimo Paci and Blerim Dzemaili came in with a pincer movement to bring down Paulo Vitor Barreto. Replays might suggest, though, that Dzemaili got to the ball first and Barreto ran into his foot.
Bari have had bad luck with spot-kicks recently and it continued when Alessandro Parisi placed it wide of the upright with the inside of his left foot.
Barreto was very unlucky for the home side after the restart, as he went on a mazy run through the penalty area and his finish was deflected on to the base of the post.
Bari are already dealing with an injury crisis and it got worse, as Barreto pulled up while running and clutched the back of his thigh. He was in agony and stretchered off, so it could be a very long lay-off for the Brazilian.
The Marques cross found Crespo for a free header, but it only shaved a coat of paint off the far post.
Bari's situation deteriorated even further, as Andrea Masiello was shown a straight red card for a crunching tackle on Marques. He took a running jump and went in with his studs up, so the decision was entirely understandable. It sparked a scuffle and Sergio Almiron had to be led away, as he was livid and repeatedly kicked the advertising boards.
Yet it should've been 1-1 with 11 minutes left on the clock, as Massimo Donati nodded on a corner kick for Andrea Raggi to balloon over from six yards!
Bari continued shooting themselves in the foot, as Donati received a second yellow card for dissent and sarcastically applauded the officials on his way off the field.
Bizarrely, Bari continued to pour on the pressure with nine men against XI, as Antonio Mirante had to palm away a Belmonte snapshot.