Despite a tough night at the Artemio Franchi Stadium, with Fiorentina winning 2-1 in the second leg, Palace progressed 4-2 on aggregate.
Palace captain Henderson was beaten by a stunning strike from Cher Ndour not long into the second-half, which raised the nerves of the travelling fans.
But he went on to make a series of excellent saves as the Eagles rode out the storm and saw out the final ten minutes with relative comfort.
"It's a great moment for them," Henderson told TNT Sports. "100%. They've stuck by us in the difficult times this season and hopefully we can go on and deliver something really special.
"I think it was a tough game tonight, it was very tough. You don't really know how it'll go. 3-0 can be a dangerous scoreline and we've managed to get through, so who cares.