Gibbons, turning out for local team Dimension Data, launched another charge in a sprint for the line on the 229km leg between Forli and Reggio Emilia.
Though the 22-year-old rider narrowly failed to reach the podium, it was his fifth top-eight finish on a spectacular debut at the Grand Tour race.
Fernando Gaviria of Colombia (Quick-Step Floors) won the stage, while Dutch rider Tom Dumoulin (Sunweb) remained more than two minutes clear of his nearest opponent in the general classification (GC). Jacques Janse van Rensburg was the top Dimension Data rider in the overall standings, lying 39th in the GC with nine stages remaining.
Spaniard Omar Fraile, who won the 11th stage for the South African outfit, was rewarded for his hard work on the climbs by earning the King of the Mountains jersey.
The 13th stage on Friday will take the peloton 167km from Reggio Emilia to Tortona.