The very first time they played it was on January 20, 1972, though they stopped somewhere in "Money" due to technical problems. They played it all but 'Eclipse' the next night -- 'Eclipse' had yet to be written. In its place, they played a instrumental jazzy song. Roger didn't feel this was a dramatic enough finale, however, and wrote 'Eclipse' for the Bristol show in early February (the 5th, according to Miles). The Bristol show was then the first time the whole album was performed.
Album is italicized because early performances were substantially different from DSotM as it was eventually recorded and released. Early renditions of Dark Side of the Moon had a jam version of 'On the Run' (instead of the synthesizers), a slower version of 'Time,' and a vocal-less, organ-based 'Great Gig in the Sky' with a tape of preachers running in the background.