Rambutan (Nephelium lappaceum L.) peel (RBP) is discarded as the main by-product during processing of the fruit. Increasing attention is now paid to the valorization of RBP for the recovery of valuable compounds. Geraniin, ellagic acid, quercetin, and rutin are the main phenolic compounds found in methanolic RBP extract. Extracted rambutan peel powder (ERPP) is used to evaluate the oxidative stability of soybean oil stored at 4 and 30 °C in the dark and light and deep fried with potatoes at 160 °C. Tert-butylhydroquinone (100 µg g−1 oil, TBHQ) serves as positive control. Oil supplemented with ERPP of 1000 µg gallic acid equivalents (GAE) g−1 of oil shows positive effects on the retardation of the oxidation process during storage in comparison with oil without addition. During deep frying, either ERPP (1000 µg GAE g−1) or TBHQ retards the lipid oxidation of oil. Levels of thiobarbituric acid reactive substances of potatoes fried in oil fortified with the extract and TBHQ (0.4–0.59 µg g−1) are much lower than those without the extract (1.31 ± 0.10 µg g−1) (p < 0.05). Therefore, RBP extract exhibits favorable antioxidant effects and can be used for effectively inhibiting lipid oxidation in oil during storage and deep frying.