All I can think of so far is
~Accidents Will Happen (Elvis Costello) and Bic Runga (Sway) [their openings]
~Starman (Davd Bowie) and Somewhere over the Rainbow (Wizard of Oz) [the start of the chorus]
~Got to Get You into My Life (The Beatles) and We Gotta Get Out Of This Place (the Animals) [the chorus and their names]
~And of course that song that George Harrison got in trouble for ripping off in his My Sweet Lord.
The more seemingly bizarre the pairs are the better!