Inciarte hit ground ball to the hole at second that was fielded by second baseman Brandon Phillips, who threw to pitcher Mike Leake covering first base. Leake caught the ball and stepped for the base at the same time Inciarte did.
First base umpire Kerwin Danley called Inciarte out and Gibson immediately challenged the call.
After a brief review, it was ruled that the play would stand meaning there was not clear and convincing evidence to overturn the call.
"I saw [first baseman Roger] Bernadina wasn't going to get back so I had to get there quick," Leake said. "Their guy came up on me pretty quick. I wasn't expecting it to be that quick. It kind of caught me off guard when we both touched the bag at the same time."
The D-backs have challenged eight calls this season and had two overturned.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.