11:03 AM PT -- Turns out Drake didn't technically have to "rent" out the stadium ... a source with the team tells us his date night was all made possible thanks to a substantial donation he made to the Los Angeles Dodgers Foundation.
Drake took full advantage of the Dodgers being out of town Thursday ... setting up a date on L.A.'s field with Johanna Leia -- and the whole thing looked like it was taken right out of a Drake song.
While Justin Turner and the boys were in Miami wrapping up their series with the Marlins ... the rapper took advantage of the opportunity to borrow their arena for a cozy date night -- and it's clear, he balled out for the occasion.
A helicopter camera spotted the 34-year-old at a table with Leia near the dugout on the third-base side of the field ... and there was a white table cloth, multiple dishes, flowers and even a personal bartender for the couple.
In fact, the two appeared to have gotten personalized Dodgers jerseys for the occasion ... with Leia rockin' hers right at the table!