After Trundle had put City ahead, Preston were twice denied by Brazilian keeper Adriano Basso.
Even after McIndoe made it two, Preston had their chances, Chris Brown volleying over and Neal Trotman heading wide.
Six minutes into the second half, however, Noble made them pay and the game was settled.
Interview: Bristol City striker Lee Trundle
The hosts continued to press, however, with Trotman having to block an Adebola header before Marvin Elliott shot wide from the edge of the area.
Preston boss Alan Irvine threw caution to the wind by making a triple substitution shortly before the hour mark bringing Craig Beattie, Darren Carter and Simon Whaley into the action.
City remained the dominant side, though, and Trundle was unfortunate not to collect a second when his effort from outside the area crashed against the crossbar.
Preston keeper Andy Lonergan thwarted substitute Lee Johnson late on, but it was a comfortable day for The Robins, who can now look forward to tackling The Eagles.
Bristol City boss Gary Johnson: "Lee Trundle worked his socks off and looked a real threat. We played well in defeat at Sheffield United in our previous game, and carried that on here.
"We know what to expect from any Neil Warnock side, and Palace are in very good form. But we are proud of finishing fourth in the Championship after 46 games and will go there next Saturday in confident mood.
"We were going to look forward to the play-offs whoever our opponents were, and the way we played today gives us great heart."
Preston manager Alan Irvine: "That wasn't the sort of performance that got us out of trouble.
"We have done well recently by looking good when the opposition had possession. Here it was far too easy to create chances against us.
"But the players still deserve a lot of praise, because we were cast adrift at the bottom of the table not so long ago."
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