We describe a cross-lingual adaptation method based on syntactic parse trees obtained from the Universal Dependencies (UD), which are consistent across languages, to develop classifiers in low-resource languages. The idea of UD parsing is to capture similarities as well as idiosyncrasies among typologically different languages. In this article, we show that models trained using UD parse trees for complex NLP tasks can characterize very different languages. We study two tasks of paraphrase identification and relation extraction as case studies. Based on UD parse trees, we develop several models using tree kernels and show that these models trained on the English dataset can correctly classify data of other languages, e.g., French, Farsi, and Arabic. The proposed approach opens up avenues for exploiting UD parsing in solving similar cross-lingual tasks, which is very useful for languages for which no labeled data is available.