Schweinsteiger opened the scoring with a low shot after Franck Ribery and Arjen Robben had combined to create the chance.
Valencia rarely tested Manuel Neuer in the Bayern goal and the hosts were rewarded for their superiority 14 minutes from time when Toni Kroos rifled in from 25 yards.
But Bayern were made to endure a crazy finish as Nelson Valdez pulled goal back with an injury-time header, before Adil Rami received a second yellow card for a tug on Robben in the box. But the late drama was complete when Mario Mandzukic's penalty was saved.
Just four short months ago, Bayern Munich were denied the glory of a Champions League title on their own turf. A night that was supposed to be one of the greatest in the German club’s already illustrious history turned into a nightmare – and the wound is still healing.
But the acquisitions of Javi Martinez and Xherdan Shaqiri are shrewd ones, and the former’s central partnership with Schweinsteiger gives Bayern a new look as they look to erase the painful memories inflicted by Chelsea in May.
Martinez compliments Schweinsteiger well, and the pair controlled the midfield battle against the beleaguered Daniel Parejo and Tino Costa, who were never able to exert their influence on the game as Bayern created several key openings against the side they beat in the 2001 final.
The first fell to Kroos, chosen ahead of Thomas Mueller in the hole behind the striker Claudio Pizarro. Shifting the ball onto his left foot 25 yards from goal, the forward thumped a left-footed shot at goal that Valencia goalkeeper Diego Alves did well to parry to his left.
Robben could have opened the scoring, but turned provider when Bayern eventually underlined their dominance with the opener seven minutes before the break. Found by Ribery, after the Frenchman’s driving break, Robben slotted in Schweinsteiger on the overlap – and he drilled a low shot into the far corner with the help of slight deflection off Aly Cissokho.
Bayern coach Jupp Heynckes replaced Ribery with Mueller at the break and the German created a chance from which Bayern should have been awarded a penalty. Mueller’s pull-back found Kroos, who was upended by Costa, yet nothing was given.
Valencia continued to sit back and wait for the counter-attack, and it almost worked for them when Sofiane Feghouli outmuscled Dante to squeeze in a shot, but Neuer was alert at his near post.
But that was as close as Valencia came before Kroos put daylight between the sides with a thunderous strike that flew beyond Alves.
But just as Bayern appeared to be cruising to a routine victory, Valdez found space in the box to head in Jonathan Viera’s cross from the left after a short corner.
The final moments were even crazier though, as Rami was dismissed for tugging back Robben in the box – only for the in-form Mandzukic to see his penalty saved.
It was a frantic end to a game that Bayern dominated, and last season’s beaten finalists took the first step in repairing the wounds of that defeat in May.
MAN OF THE MATCH
Toni Kroos - Linked midfield and attacking superbly. Capped fine forward display with thunderous second strike, which put the game beyond Valencia.
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