Bruce played the song in 1971 and 1972.
1971-09-01 - GARFIELD PARK, LONG BRANCH, NJ
I've got to have you baby is known to have been performed at least once in Bruce Springsteen's early years (pre-October 1972). Very little is known about shows from this early period, and therefore, the song may have been played on some more dates. The only known cover performed was during one show, triple bill, with the five-member Bruce Springsteen Band headlining. The support acts for this show were originally Sweet Chariot and Tumbleweed, but it appears that the latter were replaced at the last minute by The Joe Hagstrom Squeak Band. This was an outdoor show orchestrated by Tinker West’s Blah Productions. Garfield Park is located at the intersection of Broadway and Ocean Ave, near the ocean. Their version is radically different from the original one by The Pretenders. An obscure 1956 R&B single by Jimmy Jones & The Pretenders, covered by The Bruce Springsteen Band around Jan-Feb 1972 at Challenger Eastern Surfboard Factory, Highlands, NJ, during rehearsal sessions.that were frequently conducted at the factory . There’s also a version of the song on the 'Challenger Eastern Surfboard track list' :
Challenger Eastern Surfboards Rehearsals:
Bruce Springsteen wrote numerous songs in 1971 but did not record any material in a professional recording studio during that period. However, studio rehearsal sessions were frequently conducted at the Challenger Eastern Surfboards factory in Highlands, NJ, in 1971 and early 1972. The primary purpose of the sessions was not to make audio recordings, but to prepare for live shows. So only a fraction of this extensive body of rehearsal sessions was ever recorded, and when they were, it is an unfortunate reality that the reel-to-reel tapes made at Challenger Eastern were often erased and reused to record live shows. It should be noted that this is not Challenger's more famous Wanamassa, NJ factory location, the one that Springsteen had lived at and rehearsed in during the 1969-1971 Child and Steel Mill era. Tinker West had relocated that factory to Highlands, NJ in mid-1971 and had then constructed a more professional rehearsal room for the various bands he managed. It also included a control room like a regular studio. Fortunately, high-quality audio of one Challenger East session is known to exist – a continuous 8-song / 83-minute segment of a rehearsal that took place in early 1972 at Challenger Eastern Surfboard. The recording was engineered and produced by Carl "Tinker" West. The session line-up was Bruce Springsteen, Steve Van Zandt, David Sancious, Garry Tallent, and Vini Lopez.