Many spell descriptions specify a melee spell attack. Examples are Bigby's Hand, Contagion and Inflict Wounds. A melee spell attack is a melee attack.
Didn't mean to imply otherwise, the rules pretty clearly say 'melee attack' not 'melee weapon attack' or anything more specific.
'Many' is relative. Most spells don't use attack rolls, at all, not even most spells that inflict damage. Nor do all spells that use melee attack rolls inflict damage.
If you want to argue that the Rules as Written imply that using each of those spells to reduce a victim to 0 hps give you the option of rendering him unconscious, though, you probably shouldn't expect consistent results. Contagion doesn't do hp damage, so you wouldn't reduce someone to 0 hps via it's 'melee attack,' anyway. Inflict Wounds I wouldn't waste a lot of time trying to 'prove' you wrong, as DM, I'd just rule that you couldn't. I'd feel less inclined to rule that way when you're slapping someone around with a giant hand made of force.
Another example, Shocking Grasp, I'd have no trouble with - 'shocking' someone unconscious seems fine in a way that incinerating or necrotizing them to unconsciousness doesn't.
Ultimately, spells are pretty darn versatile, there are spells that can deal with an enemy without killing him, already. Just prep one of those if it's something you think you might want to do.