Sam & Max Save the World: Just You and Me (and Ted E. Bear)
"N O M A F I A, Oh Baaaaby..."
There are four songs in Sam & Max Save the World, and this is number two. It appeared in The Mole, The Mob, and The Meatball (episode 3), and the lyrics were penned by David Grossman (unless I'm remembering it wrong...it's been awhile).
There should be more songs with vocals in games!