After a quick look on PubMed, I found a meta-study on the effects of melatonin in various contexts, published in Nutrition Journal (it's open access, so the article is freely accessible without any kind of academic subscription). It makes a "weak recommendation in favor of melatonin use for rebalancing the sleep-wake cycle in people with jet lag."
Here are the meta-study's results concerning jet lag (emphasis mine):
Eight [37–44] RCTs with 972 total participants characterized melatonin use for counteracting jet lag. Almost all of the studies were of high (+) quality [37, 39–44], with the exception of one poor (−) quality study , which favored neither melatonin nor control, despite a large sample size (n = 339). Of the seven high (+) quality studies, one  favored neither melatonin nor control. The remaining six [37, 39, 41–44] RCTs favored melatonin, including two [42, 43] large studies (n = 320  and n = 160 ) and one  which noted a limitation that melatonin increased tiredness the next morning. Melatonin appears to be relatively safe based on the six [38, 39, 41–44] studies that reported adverse events, citing occasional, but not serious adverse events and interactions. Based on the high quality and favorable results reported, the [subject matter experts] concluded that in a jet lagged population, further research may have an impact on the confidence in the estimate of the effect, and as such, provide a weak recommendation in favor of melatonin use for rebalancing the sleep-wake cycle in people with jet lag.
Costello, R. B., Lentino, C. V., Boyd, C. C., O’Connell, M. L., Crawford, C. C., Sprengel, M. L., & Deuster, P. A. (2014). The effectiveness of melatonin for promoting healthy sleep: a rapid evidence assessment of the literature. Nutrition Journal, 13, 106. http://doi.org/10.1186/1475-2891-13-106