After trying various solutions, I finally figured out the one that works like a charm!
Run the following command from the project root directory:
    npm install request
//Enabling CORS on ExpressJS
app.use(function(req, res, next) {
res.header("Access-Control-Allow-Origin", "*");
res.header("Access-Control-Allow-Headers", "Origin, X-Requested-With, Content-    Type, Accept");
next();
});
//Making an API call from NodeJS server
// Posting field (json object) to mocky.io
    var request=require('request');
    var mockyPostRequest = {
        url: 'http://www.mocky.io/v2/596a5f03110000920701cd92',
        method: 'POST',
        headers: {
            'Content-Type': 'application/json'
        },
        json: field
    };
    request(mockyPostRequest, function(err, res, body) {
        if (res && (res.statusCode === 200 || res.statusCode === 201)) {
            // Logging the post data on the console
            console.log(body);
        }
    });
I used following as the reference: 
https://enable-cors.org/server_expressjs.html
Thanks everyone for replying.