Piatti came close to handing his side the lead in the 30th minute when he struck at goal and forced Steve Clark into a diving stop, pushing the powerful shot over the bar.
The Impact took the lead in the 40th minute when Piatti drove at the Columbus defence and pulled defenders one way and then the other, before firing a left-footed shot past Clark into the bottom corner.
After the break, veteran striker Marco di Vaio could have doubled his side's lead when he raided down the right and cut in from the flank, but he put his effort into the side netting.
The Impact had a great counter-attacking chance to wrap the game up in the 83rd minute, as Piatti drove his side downfield and slid a pass to Andres Romero, but the midfielder put his shot well wide of the target.
Piatti secured the win in stoppage time as he collected a loose ball in the penalty area and powered a shot past Clark into the top corner following a break from Di Vaio.