Background: Alzheimer’s disease (AD) and Parkinson’s disease (PD) are multifactorial neurodegenerative disorders that are mostly treated with drugs inhibiting key enzymes of cholinergic and aminergic neurotransmission, such as acetyl and butyryl cholinesterase (AChE, BuChE) or monoamine oxidases (MAO)-A/B, and of Aβ 1–40 aggregation. Diet plant components with multitarget functions are promising compounds in the prevention of AD and PD. Our aim was to identify neuroprotective compounds from Annurca apple polyphenol extract (AFPE). Methods: AFPE was fractionated by gel filtration, and the eluted peaks were subjected to chemical analyses (i.e., RP-HPLC and mass spectrometry), determination of inhibitory enzyme activity and cell effects by MTT, and morphology assays. Results: In AFPE, we identified thaumatin-like protein 1a, belonging to the pathogenesis-related protein (PR) family. This protein showed the best inhibitory activity on AChE, MAO-A (IC50 = 5.53 µM and 1.71 µM, respectively), and Aβ1–40 fibril aggregation (IC50 = 9.16 µM), compared to AFPE and other polyphenol-containing fractions. Among the latter, Peak 4 reverted Aβ fibril formation (IC50 = 104.87 µM). Moreover, thaumatin-like protein 1a protected AGS and MKN-28 cells from serum-deprivation-induced stress conditions. Conclusions: We showed that AFPE exerted neuroprotective functions not only through its polyphenols but also through thaumatin-like protein 1a, which acted like a multitarget molecule.