aubergine from Persian بادنگان bādingān probably borrowed from Middle Indic *vātiñjana-, vātingana-, compare Sanskrit hastivātiṅgaṇa "eggplant"
bandanna from Hindi बांधना bāndhanā "to tie"
bangle from Hindi बंगरी baṅgarī "glass bracelet"
banyan from Gujarati વાણિયો vāṇiyo "member of Bania caste; Bania; merchant; shopkeeper"
beriberi from Sinhala බැරි bäri "inability, incapability, impossibility"?
bungalow from Hindi बंगला baṅgalā "belonging to Bengal", because houses of this style were "Bengali-fashion" houses
cheetah from Hindi चीता cītā
chintz from Hindi छींट chīṇṭ "spot, speck, stain, blot; spattering, splash"
chutney from Hindi चटनी caṭanī from चाटना cāṭanā "to taste"
dinghy from Bengali ডিঙ্গি ḍiṅgi "small boat"
juggernaut from Hindi जगन्नाथ jagannāth "Krishna" from Sanskrit jagannātha "lord of the world"
jungle from Hindi and Marathi जंगल jaṅgal "desert, waste, forest"
loot from Hindi लूट lūṭ from Sanskrit loptra "stolen property, plunder" from lup "to seize"
mandarin from Spanish mandarín borrowed from Malay menteri borrowed from Sanskrit mantrin "king's counsellor, minister"
nark probably from Romani nāk "nose"
opal probably from Sanskrit उपर upara "posterior, later; the lower stone on which the soma is laid" from upa "below"
pal from Romani phral "brother"
palanquin ultimately from Sanskrit palyaṅka, paryaṅka "bed, litter" (OED)
Parcheesi from Hindi पच्चीस paccīs "twenty-five"
pepper from Indic, compare Sanskrit पिप्पली pippalī "long pepper" (much more)
posh perhaps from Romani paš "half"
punch the drink, from Hindi पाँच pāñc "five", or from Sanskrit pañca, short for पञ्चामृत pañcāmr̥ta "five nectars (of the gods), the five kinds of divine food"
shampoo from Hindi चाँपो cāmpo, the imperative of चाँपना cāmpanā "to press"
sugar possibly from Sanskrit शर्करा śarkarā "gravel, ground or candied sugar"
thug from Hindi ठग ṭhag "robber, assassin"
tourmaline from Sinhala තෝරමලලි tōramalli "carnelian"
verandah? from Portuguese varanda from Hindi बराँडा barāṇḍā, Bengali বারান্দা bārāndā (OED)
also see my list of words of Dravidian origin.