EXCLUSIVE

Justin Bieber hit speeds of 136 miles an hour in his rented Lambo just hours before his arrest ... TMZ has learned.

We've now obtained the FULL GPS speed readout for the evening in question -- not just the period immediately surrounding the arrest.

Check it out. The GPS map corresponds to the readout. At 1:23 AM Justin was on the Julia Tuttle Causeway in Miami Beach, heading toward the nightclub. He was clocked at 108 MPH and within a minute he accelerated to 136 MPH.

The red line is from the readout -- the color appears when the RPM reaches an extreme limit.

Bieber arrived at Set nightclub at 2:27 AM, stayed an hour and then drove away.

Cops claim Bieber was drag racing, but the read shows otherwise -- in the middle of the so-called drag race, he was cruising at 27 MPH -- under the speed limit.