Dear John,
It's a good question that could have different answers depending on your "parameters" -- particularly the question of direct vs. mediated translation. Anquetil-Duperron's translation of the Upaniṣads, for instance, as Prof. Lindquist just mentioned, was translated from the Persian version of Dara Shikoh.
A more extended case of such mediation could take us back to the Middle Ages, when the Pañcatantra was translated into Latin via Pahlavi and Arabic (there under the title Kalila wa Dimna). From Latin, the Pañcatantra quickly found its way into numerous other European languages: according to Edgerton (1924), it was certainly extant in Greek, Spanish, Italian, German, English, Slavonic languages, etc., before 1600. Olivelle (2009) offers a general trajectory of Sanskrit --> Pahlavi --> Arabic --> Syriac (10th/11th c.) --> Greek (11th c.) --> Latin; there is also another fascinating trajectory from Sanskrit --> Pahlavi --> Arabic --> Persian --> Spanish (ca. 1251) and Hebrew (12th c.) --> Latin (between 1263-1278). The life of the Buddha has a comparable trajectory, eventually becoming the story of Barlaam and Josephat via Arabic, Persian, Hebrew, and other languages.
In the vein of Abraham Rogerius, early Christian missionaries were of course active from the early 16th c., particularly the Jesuits. It's well-known that they were translating in the other direction (translating Christian materials into Indian languages), but I'm just not familiar enough with the materials to know about the earliest translation in the other direction. The 1610 (and onwards) Portuguese translations that Prof. Vielle mentions are certainly noteworthy in this vein. I have encountered mention (I believe by Will Sweetman) of an Anādipurāṇa that a Brahmin convert to Christianity, Manuel d’Oliveira, partially translated into Portuguese via Marathi/Konkani, ca. 1558 (mostly episodes from the Mahābhārata and Rāmayāṇa).
Adding a different kind of ambiguity to your question is when Europeans would themselves patronize translations into Persian, which would then later find their way into European languages. Rosanne Rocher (1983, pp. 48-72) tells us of Warren Hastings' commission of a Persian translation of the Vivādārṇavasetu, then translated into English by Halhed as A Code of Gentoo Laws in 1776. This is just one of numerous European-commissioned translations in this time period that were mediated by Persian (see Carl Ernst, "Muslim Studies of Hinduism?," 2003).
Hope this helps,
Shankar
Shankar Nair
Associate Professor
Department of Religious Studies and
Middle Eastern & South Asian Languages & Cultures
University of Virginia