400 Bad Request on RestTemplate POST request to Salesforce Oauth

Question

I am trying to send a POST request to https://test.salesforce.com/services/oauth2/token to retrieve the oauth access token. The response is 400 Bad Request with no info. Here's the (Java) client code:

private void authenticate() {
    RestTemplate req = new RestTemplate();        
    JSONObject oauth_req = new JSONObject();
    //JSONObject oauth_res = new JSONObject();

    oauth_req.put("grant_type", "password");
    oauth_req.put("client_id", this.CONSUMER_KEY);
    oauth_req.put("client_secret", this.CONSUMER_SECRET);
    oauth_req.put("username", this.USER);
    oauth_req.put("password", this.PASSWORD);

    String reqToString = oauth_req.toString();       
    HttpHeaders headers = new HttpHeaders();
    headers.setContentType(org.springframework.http.MediaType.APPLICATION_JSON);

    HttpEntity<String> entity = new HttpEntity<>(reqToString,headers);
    String res = req.postForObject(TEST_AUTH_URL, entity, String.class);
    System.out.println(res);
}

I have attempted this with both postForObject() and exchange() with the same results. I am certain that the body is correct, as I am able to retrieve the token with Postman. Is it possible that the issue is with my header or entity?