Schweinsteiger scored the decisive penalty which put out Real Madrid in the semi-finals last night and Neuer saved spot-kicks from Cristiano Ronaldo and Kaka at the Bernabeu.
Ronaldo had earlier scored from the penalty spot and added a second before Arjen Robben's penalty levelled the tie on aggregate and took the game into extra time.
Mario Gomez and David Alaba also scored for Bayern in the shoot-out but Philipp Lahm and Toni Kroos saw their efforts saved by Iker Casillas.
After Neuer had saved from Ronaldo and Kaka, Xabi Alonso netted his effort from the spot before Sergio Ramos fired over the bar, leaving Schweinsteiger the unenviable task of stepping up to fire Bayern into the final.
Schweinsteiger told the club's website: "Ever since it was announced that the final would be in Munich, we all had only one target: to get there.
"Now we have one more match at home, and we want to win it. The only thing going through my head was putting the ball in the net."
Neuer said he thought Bayern had been rewarded for matching Real in both legs of the semi-final, winning the home leg 2-1.
He said: "We've all worked very hard for this. In both games, we were on a par with them at the very least, and at the end of the day, we deserved to win. I was determined to save those penalties, although obviously luck plays its part."
Bayern also take on Borussia Dortmund in the final of the DFB-Pokal and Neuer hopes they can make it a Champions League and domestic cup double. He added: "It's great we have two finals ahead of us."