Hmmm...If the puppet Inca Manco reads up (or rather, has read to him) his military history a little more while in captivity under the Spaniards, and recognizes that his armies cannot directly face the Spanish cavalry as is. He therefore orders General Quizo to prevent the Spanish from crossing the Andes to Cuzco instead of attacking them at Lima. This butterflies General Quizo's disastrous defeat, and lets him stay in the Andes where he can drop rocks on the heads of any Spaniards attempting to go inland.
Then, the Spaniards besieged in Cuzco lose. Perhaps more attempts to burn Cuzco succeed, and they die, or they escape and make their way to Lima. Either way, the Inca have seized Cuzco, and from there can reassert control over their empire in a big way. However, they will have to completely overhaul their way of waging war (throwing overwhelming numbers of infantry at heavy cavalry isn't going to work) and cede a lot of territory, particularly the coastal plains, some of the more accessible mountain valleys, and rebellious provinces such as those of the Canari to the Spanish.