Super Mario Bros. 3 has now been beaten in under 3 minutes in a TAS.
What happens exactly: By using a glitch that embeds Mario in the wall of the pipe's by a pixel, the game sees him as standing on the pipe's end cap and allows him to go "down" it (that it's an up-pipe doesn't matter) until he exits outside the normal map boundaries in a glitched area. There, he jumps and hits an invisible note block, which, being out-of-bounds, causes a memory write outside the normal tile data addresses that screws up the way the processor interprets memory addresses. This leads to a series of incorrect instructions being read from unintended areas of the ROM, until eventually a stack overflow causes it to start reading instructions from RAM addresses near where the x-positions of enemies are stored. By positioning the koopa shells beforehand, arbitrary code can be written in their x-positions, which the player uses to jump to the subroutine with the Princess's room.